People like best off, top 10's and other such rankings, so I prepared a personal tier list of hero abilities for units. Since I obviously did not roll all of possible heroes in campaigns yet this is not only based on the ones I actually got, but also on some theory. Feel free to disagree on the ranks and share your own ones - I 'm really curious about different experiences and ideas.

Since I based the post on Fulgrims list, which is quite old, some names/functionality might not be accurate anymore.
S Tier - insanely powerful in every situation
Double Attack - Unit gets 2 attack actions per turn. - godly ability as on best tactical bombers you can basically one turn kill targets, but works on fighters, tanks, infantry, basically anything. It's almost like having another free copy of a unit. Limited only by the presence of viable enemy units you can attack in a turn. Also increases the amount of experience gained by the unit for obvious reasons.
Ignores Entrenchment - Ignores enemy entrenchment (unit's accuracy is not affected by enemy's entrenchment level) - with this any unit attacks at full strength regardless of issues with terrain. After playing for a while it became one of my favorite heroes, since especially for vehicles this is huge and allows them to clear close terrain. Infantry with Ignores Entrenchment is basically pioneers, so it's not uncommon to have super pioneers in the form of Grenadiers or Azul Infanterie.
No Retaliation - Enemy units don't shoot back when attacked by a unit with this trait. - infantry with this trait can capture cities with little or no support. Very powerful as it not only reduces losses, but allows to take otherwise impossible fights.
On The Roll - For each enemy unit killed in the current battle, this unit gets +1 attack till the end of the battle - those overruns just got out of control even more. It just requires a specific tanks to work, with lots of ammo and good initial stats. Blocked for the player in campaigns for a reason. Currently not possible to roll on a hero in non-modded campaigns.
Rapid Fire 2x - Makes 2x more shots than normal and consequently deals 2x damage to the target. This trait does not affect ammo spending, the unit still consumes 1 ammo per attack. - convinced to move up a tier in line with Double Attack being very similar. Better on tanks, recons, infantry and AT guns, while Double Attack is better on planes, artillery and AA guns since it allows to spread the firepower between targets, while with Rapid Fire 2x you usually want to concentrate it on one target. Currently not possible to roll on a hero in non-modded campaigns.
Steamroller - Any kill triggers an overrun - has to be earned the hard way, but it then becomes a powerhouse, chaining kills regardless of terrain type. Requires the Overrun her or trait to function! Currently not possible to roll on a hero in non-modded campaigns.
Vigilant - Prevents enemies from using unit's Close Defense rating - it makes combat much, much easier and safer for any tank or vehicle. Used correctly it allows to bring heavy equipment to every fight, block city or forest hexes wit unmovable, monstrous units and perform attack from otherwise impossible directions.
Zero Slots - Unit slot cost is reduced to zero - arguably the best hero in the game. Applied to a 21 cm artillery or some other slot intense unit can allow for 2-3 more units, adding half-tracks for all your infantry or bringing all the bridge engineers, recon planes and other 1 slot support you ever dreamed of.
A Tier - make game changing differences for units
Butcher - +5 attack against infantry units - on units with high soft attack it can be insane, especially on tanks where it further helps trigger multiple overruns. As it is often more valuable to just take out infantry instead of capturing it, this trait is better than Tank Killer.
Camouflage - Can only be detected by recons or adjacent ground units - AT and AA support units love this due to AI limitations, but any unit can use this hero, just not all will benefit from the ability equally.
Crippling Blow - +5 attack against full strength units - very universal attack bonus, great for tactical bombers. The first hit is often the most important one as it's done by the best unit, so this greatly helps if no support fire is available to soften up the target.
Envelopment - Prevents enemy units from retreating, so they surrender instead. - more prestige is always welcome, as is easier unit capturing, especially for those who do it on higher difficulty. Combined with Overwhelming Attack it's S+ tier no questions asked and best combo there is, causing instant surrenders of unfortified units that are dealt damage and gaining insane amount of equipment and prestige, easily making a difference between a net gain or loss at the end of a scenario.
Fast Deployment - Can unmount from organic transport and fire after movement - absolutely changes the way artillery and infantry can operate, providing huge movement savings. Works for all units with organic transport, but there is a trait that does the same if this idea sounds appealing to someone. However, it just compensates for inherit movement weakness, it does not add combat strength.
First Strike - Unit always attacks first - I would prefer them to not shoot back at all, but this is still great sinc eit works on the defense contrary to No Retaliation. Best on fighters, tanks and AT guns, due to the way shooting first often results in devastating losses and prevents the enemy from hitting back efficiently.
Hit And Run - When attacking, enemy units with lower initiative do not shoot back - everything that minimizes losses so efficiently is a godsend.
Lethal Attack - Half of suppression caused by this unit is converted to kills - AA's best friend. Not so amazing with AA veteran trait. Also great on tactical bombers.
Overrun - Can destroy ("overrun") weakened enemy units without spending move or attack actions. The way it works is, after an overrun attack, move and attack actions of the unit will be replenished. - huge ability and giving it to units other than tanks can be amazing.
Overwhelming Attack - Any damage to enemy units is enough to force the to retreat. - seems great, but in rare cases can be liability more than a benefit. However, for capturing units it's ideal, especially with combination with other heroes.
Rapid Fire 1.5x - Makes 1.5x more shots than normal and consequently deals 1.5x damage to the target. This trait does not affect ammo spending, the unit still consumes 1 ammo per attack. - great bonus, that's a tank's best friend for overrun purposes.
Reduced Slots - Unit slot cost is reduced by 50%- can save enough prestige to field another unit or two. Ranked A only since there's an even better variant.
Shock Tactics - When attacking, pins enemy unit in place by destroying all its movement points. - great for capturing, but can be a liability sometimes when you want the unit to retreat. Very similar to Envelopment, but actually better (I'd rate it A+), since it applies to a wider selection of units. Envelopment has to be used on the specific unit making the attack that would force the retreat, while Shock Tactics can be applied before, by for example artillery or strategic bombers and allow other units to deal the finishing blow.
Tank Killer - +5 attack against tanks - always good, on any type of unit, but for obvious reasons tanks, AT and tactical bombers use it best. In AO 1939 don't be surprised in the Bzura scenario however with a particular opponent who can surprise panzers like crazy... As the name suggests it works against tanks, not all hard targets.
B Tier - efficient heroes that provide measurable bonuses
Aiming Assistance - +10% accuracy to all adjacent friendly units - accuracy is king and turning another unit into a semi-recon can quickly add up over the course of a scenario and campaign. It also helps the unit gain experience from the assistance, as well as gives back line units extra utility. One of the bast ways to lever up AT and AA guns early.
Artillery Support - Provides support fire to adjacent friendly units attacked by enemy's unarmored units (with 'Soft' target type). - very useful since any form of support can really help units from being exposed to major losses, but has to be put on a unit that is going to be actively supporting infantry anyway (Panzer IIIN for example?). On largest guns that just have Counter Battery Fire seems like a waste actually, since I tend to put those on hills or further back, so the ability would not trigger.
AT Support - Provides support fire to adjacent friendly units attacked by enemy's armored units (with 'Hard' target type).- same as Artillery Support, with the added bonus of working nicely on towed artillery early game and on tanks perfectly the entire game.
Bridging Unit - Acts as a bridge when positioned on a river - now that's some major mobility bonus for the rest of the army! The only reason I'm not putting it higher is because not all maps are structured in a way to utilize a unit like that. But then you might just not deploy it for such scenarios. Currently not possible to roll on a hero in non-modded campaigns.
Close Combat - Has access to enemy unit's Close Defense rating when fighting in close terrain. - quite an improvement, but armored units don't want to fight in Close Terrain anyway when possible. Currently not possible to roll on a hero in non-modded campaigns.
Consolidator - Can consolidate more than normal strength into a single unit, thus increasing maximum overstrength which the unit can have by +5 - can create huge super-units, but at a massive prestige cost, as it works best on high power units. If combined with Reduced Slots it can easily be A tier and with Zero Slots clear S tier, but without them it is just that little bit too expensive.
Double Move - Units gets 2 move actions per turn, without increasing the number of movement points. - tactical bomber best friend. can allow to move after bombarding, so another unit can finish the job. Double Move and Double Attack on one unit is just silly.
Exterminator - +5 attack against units below 50% strength - I've heard you like overrun, so I've added more overrun to your overrun. Less useful as time goes by and units become more powerful, but shines on slightly weaker units and early into the war. Also not as good as bonus vs. full strength units, as those wounded are usually also already suppressed.
Fast Rebase - Aircraft does not spend movement actions on rebase - I initially thought the effect is just going to be a few extra attacks for aircraft in the course of each scenario. Boy I was wrong! The ability to quickly transfer fighters on large maps can make a difference between getting bombarded for a few turns or not. I can also see this great on my own bombers that can now respond to threats appearing out of nowhere - especially experienced hero enemy units that still remain squishy against a Ju 87.
Field Repairs - Restores one point of strength every turn the unit did not attack. Applies to vehicles. - prestige savings when moving from one target cluster to another. Not that much to remove replacement entirely, but will help heal those 1-2 power hits. Also, by the end of a scenario with forces spread out, it is not impossible to heal even more if there is not much to attack. Can also help use captured units with very limited parts, as it does not use the up. Does not work on planes. Might not be that powerful, but it's the only way to reliably keep some rare vehicles running in the campaign.
Flag Killer - +5 attack when attacking enemy flags - infantry best friend, a point can be made about strategic bombers and artillery as well. Map dependent however, so not as universal as other attack bonuses.
Ignores ZOC - Ignores zone of control (ZOC) projected by enemy units when moving - sweet mobility add-on to any vehicle that can help encircle targets and reach artillery hidden behind fortifications.
Legendary - Generates 50 prestige per turn - that's a lot of prestige. Fixed in the latest version after some issues earlier.
Lightning Attack - Immune to all types of support fire - saves a lot of tactical preparation before attacking. Best on tanks, tactical bombers and infantry as these three are most often fighting against support fire.
Phased Movement - Can move in steps within its movement point limit. This ability also allows the unit to sneak through enemy's zone of control. - best tank movement bonus, also nice on cavalry units.
Precision Weapon - +20% base accuracy - great, but gets less impactful as experience grows. Currently not possible to roll on a hero in non-modded campaigns.
Provocator - Adjacent enemies attacking other friendly unit will attack this unit instead - best way to escort artillery and bombers. Also a way to set up semi-ambushes. Put it on the tank with heaviest armor possible or on infantry that will always stick to close terrain. Used correctly, can be one of the best abilities in the game, but is reliant on support, terrain, and the AI being silly.
Recon - Enemy units adjacent to recon are attacked by other friendly units with +10% accuracy (+3% for each of recon's stars) - adds up nicely, more recons are always welcome. Another good way to earn extra experience on units.Currently not possible to roll on a hero in non-modded campaigns.
Scavenger - Captures 2x equipment from surrendering enemies - in theory needs to be actively used to capture units, so not something I'd be willing to rank S, as I'm just doing the capturing as a side activity anyway. However, if you really like capturing, you will probably just take Trophies of War general trait, so this makes the hero redundant.
Unyielding - Unit cannot be suppressed by enemy fire - quite good for taking out fortified cities and other close terrain positions behind an artillery wall.
C Tier - situational usefulness, does not hurt to have them on a unit
Aggressive Counterattack - +3 attack when defending - can help on tactical bombers with better air attack (Bf 110), or just as a general buff to any unit, but that's just a basic passive. It can deter enemy attacks and thus while not spectacular, it will always have at least some impact.
Avenger - Gets attack bonus for each point of lost strength - you really do not want to take losses and even if you do, you probably do not want to be attacking with a severely wounded unit. Works nicely on overstrengthened units and... armored trains that attack as a single unit regardless of damage.
Ambusher - Always triggers an ambush when attacked - amazing defensive bonus, but the question is will the unit get attacked in the first place, so not reliable enough. Currently not possible to roll on a hero in non-modded campaigns.
Bunker Killer - +5 attack against structures - very nice in base game, but in DLC most structures are to limit access to allied deployment zones and not actually meant to be attacked... so far by AO 1939... Currently not possible to roll on a hero in non-modded campaigns.
Cheap Replacements - Replacements in battle cost as on deployment phase - can save quite some prestige, but I prefer just not to incur many losses.
City Fighter - Combat bonus in city terrain - map dependent and mostly for infantry anyway. Currently not possible to roll on a hero in non-modded campaigns.
Combat Luck - Combat results can never be worse than predicted - depends on settings. I found it to be useful on fighters to minimize the need of spending time on replacements.
Counter Battery Fire - Will fire at any attacking artillery unit within its firing range. - there are good artillery units that do not have this and could certainly benefit from the ability, but light artillery will not contribute much.
Distraction - Enemy units next to this unit do not provide support fire - for fighters to allow safe bombardment and maybe recons or infantry to disable AT guns.
Double Mass Attack - When participation in Mass Attack, contributes double effect. - while nice, it's still mostly just the case of initiative, so not that critical. Currently not possible to roll on a hero in non-modded campaigns.
Double Support - Provides support fire twice for each enemy attack - whatever this unit supports will almost never be actually efficiently attacked, but I like it on units with at least 6 ammo to be really effective. With 4 it's still nice, but can run out early in a pinch and actually be counter productive when the ammo runs dry and an unsupported unit gets killed. Do not combine with Camouflage on AT guns for that very reason!
Entrenchment Killer 2/3/4 - Destroys 2/3/4 points of entrenchment with every attack - artillery already does the same thing and other units aside from planes would get shot back. For fighters that after getting air dominance or at least superiority ten to get bored and start looking for easy targets and also for tactical bombers as there not always will be a viable exposed unit to take down. The lever 4 variant could be brought up to tier B.
Expert Recon - Provides 3x accuracy bonus on adjacent enemy units - not tested, however the bonus seems a bit overkill. Currently not possible to roll on a hero in non-modded campaigns.
Expert Support - +20% accuracy when providing support fire - quite a large bonus, can see the crippling potential on high power support units.
Famous - Generates 20 prestige per turn - that's a lot of free prestige. Gets better the higher the difficulty and the longer the campaign.
Fast Learner - 2x faster experience growth - there are units such as fighters or AA/AT guns that are notorious for slow experience growth, helps new units catch up to the rest of the core.
Fearsome Reputation - All adjacent enemy units get +3 suppression at the beginning of their turn - good siege/surrender ability, but since you need to stay next to the unit, it's not always going to affect multiple ones when it is most effective best for either infantry or heavily armored tanks. Requires careful planning and time, with the latter not always available.
First Aid - Restores one point of strength every turn the unit did not attack. Applies to infantry. - same as Field Repairs. On one side arguably better, since infantry is more prone to damage, but it also does not have the same benefit of reparing units with limited parts.
Fierce Fighter - +1 attack for each adjacent enemy unit - requires some foresight in unit placement, but can nicely add up. Mostly for gorund units, but a fighter can get a nice bonus in an enemy swarm as well.
Leadership - +1 initiative to all adjacent friendly units - will come into action often, but with a tiny benefit. Good on support units as it can be provided from the second line.
Liberator - 2x prestige for all flags captured by this unit - another prestige generator, but a bit less reliable than most. The high roll on a capture streak for recons is great however.
Low Altitude Attack - Anti-Air units with this trait can access Close Defense of attacking aircraft with the same trait. - can provide significant upgrade to 88mm AA guns, but it all depends on the scenario and situation. Currently not possible to roll on a hero in non-modded campaigns.
Prudent - Gets defense bonus for each point of lost strength - A pain to fight against, not that exiting to get. On higher difficulties you can use this to get an almost indestructible unit, so might be a consideration as there are some tricks to that with overstrengthened units, but unless they also have Zero Slots, they will be expensive to use.
Readiness - Strikes first when defending - seems like only a major thing on low defense high attack AT units (Marders for example), but on fighters it can be almost A tier in air only missions with lots of veteran enemies.
River Assault - Ignore combat penalties from rivers - bridge engineers are weak anyway and other units should for the most part try avoiding rivers, but it's often not possible, so this has the potential to come up often.
Superior Maneuver - Gets +1 initiative for each point of movement speed advantage over the enemy - for recons and fast tanks, but targets it works against will rarely shoot first anyway.
D Tier - very marginal usefulness
Evasive - Enemy units get -10% accuracy when shooting at this unit - slightly smaller losses, but that's not really too amazing.
Fighter Support - Provides support fire against enemy fighters attacking friendly bombers. Will also intercept enemy bombers attacking ground units in adjacent hexes. - air attack of tactical bombers on German side that could use this is not that amazing, but this has potential in an allied campaign. Currently not possible to roll on a hero in non-modded campaigns.
No Retreat - Unit never retreats - can sometimes help hold the front line, but rare to mater at all. That said, when it does come into play, it can save a mission...
Resilient - Cannot lose more than half strength in one go - very situational, but I can imagine how it may save a unit at least once per game.
Skilled Recon - Provides 2x accuracy bonus on adjacent enemy units - has to go D - I ranked Expert Recon at C. Currently not possible to roll on a hero in non-modded campaigns.
Skilled Support - +10% accuracy when providing support fire - one rank below expert variant, can be received as part of the awards system for units.
Smart Entrenchment - Gets 2x bonus from entrenchment - in some defensive conditions, maybe. However scenarios for Germany are mostly being on the attacking side, even later in the war. Currently not possible to roll on a hero in non-modded campaigns.
Survivor - As long as this unit has more than 1 strength, it will always survive enemy attack - nice, but mostly earned by messing up and having your unit attacked multiple times, as a specific award.

Tenacious Defender - +1 defense for each adjacent enemy unit - too situational for my tastes, unless maybe for artillery just for the sake of it and recons that might get surrounded.
Thorough Preparation - Initiative bonus +5..+1 on the first five turns of every mission - good for those fast breakthroughs in inital turns, but I prefer permanent bonuses.
E Tier - curiosities that do their job, but rarely matter at all
Ignore Mass Attack - Immunity to Mass Attack - will come in handy once in a blue moon. Currently not possible to roll on a hero in non-modded campaigns.
Learns From Mistakes - 3x experience for suffered casualties - ugh... Fast Learner is nice, this is just painfully slow and hard to reliably get any usage of and almost never worth the trouble and prestige.
No Surrender - Unit never surrenders - it's much better to just avoid positioning units badly.
F Tier - probably better traded for prestige...
Fast Entrenchment - Gets 2x entrenchment speed - I mean, in defensive scenarios where you need to relocate quickly... maybe... Currently not possible to roll on a hero in non-modded campaigns.
Fast Retreat - +2 movement points when unit's strength is 33% from maximum - just no. Currently not possible to roll on a hero in non-modded campaigns.
Ferocious Defense - Entrenchment of this unit cannot be ignored - how often do you realistically expect to defend against AI pioneers?
Safe Transit - Takes only 50% damage when caught in organic transport - or it's easier to just escort transports properly. Currently not possible to roll on a hero in non-modded campaigns.
Sixth Sense - Immune to ambushes - if I were the AI, it would be S tier for me.

Untested - I had not encountered them, they do not work, or I have too little data to justify a rank
AA Support - Provides support fire against air to ground attacks. Will shoot at any fighters and bombers attacking friendly ground units within its firing range. - does not sound too useful, air attack of non-AA units is not too amazing
Aimed Shot - not working
All Weather Combat - not working, but in theory amazing
Block Supply - not working
Deep Knowledge - not working
Defender Of People - not working
Evacuation - not working
Evasion - not working
Extended Support - not working
Ignore Ground State - not working
Last Stand - Ignores all penalties from encirclements - if it allows to resupply as well then it's amazing. If not it's F tier. Did not roll it, so not sure. Currently not possible to roll on a hero in non-modded campaigns.
Mine Sweeper - Instantly clears a minefield when given an attack order on minefield's hex - default for pioneers, but never saw this given on a hero. Very marginal if it appears at all.
No Supply - Unit does not require supply, and does not suffer negative effects of encirclement - if it means it also uses up no ammo, on certain units it could be insane. But I am not sure ho this is exactly treated by the game. Currently not possible to roll on a hero in non-modded campaigns.
Overwatch - not working
Path Finder - not working
River Crossing - not working
Splitter - Unit can be split without spending an extra unit slot. Also, unit can split and merge any number of times in a single turn. - not rolled it ever - I wonder if the general trait blocks this from happening.
Suppressing Fire - Bigger part of damage done by this unit comes in the form of suppression, not kills. Each star slightly improves the chance to outright kill the target, so experienced units with this trait become more deadly. - default ability of artillery and strategic bombers, not sure if it is actually possible to roll on a hero.
Terrain Expert - not working