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.
Fast Deployment - Can unmount from organic transport and fire after movement - absolutely changes the way artillery and infantry can operate, providing huge movement savings.
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.
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.
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.
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.
Camouflage - Can only be detected by recons or adjacent ground units - AT and AA support units love this due to AI limitations.
Crippling Blow - +5 attack against full strength units - very universal attack bonus, great for tactical bombers.
Double Support - Provides support fire twice for each enemy attack - whatever this unit supports will almost never be actually efficiently attacked.
Envelopment - Prevents enemy units from retreating, so they surrender instead. - more prestige is always welcome, as is easier unit capturing, especially fro 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.
Exterminator - +5 attack against units below 50% strength - I've heard you like overrun, so I've added more overrun to your overrun.
Hit And Run - When attacking, enemy units with lower initiative do not shoot back - everything that minimizes losses so efficiently is a godsend.
Ignores Entrenchment - Ignores enemy entrenchment (unit's accuracy is not affected by enemy's entrenchment level) - with this any grenadier becomes almost pioneers. Really powerful due to the extra stats on grenadiers.
Legendary - Generates 20 prestige per turn - that's a lot of prestige. The in-game description mentions 50, but it is actually 20 (thanks Agarwaen!).
Lethal Attack - Half of suppression caused by this unit is converted to kills - AA's best friend. Not so amazing with AA veteran trait.
Lightning Attack - Immune to all types of support fire - saves a lot of tactical preparation before attacking.
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.
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.
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.
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.
Vigilant - Prevents enemies from using unit's Close Defense rating - after a bit of digging in stats, it does make combat much, much easier and safer for any tank.
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.
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.
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.
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.
Famous - Generates 10 prestige per turn - that's a lot of free prestige. Gets better the higher the difficulty and the longer the campaign. For obvious reason it's best gained early. The in-game description mentions 20, but it is actually 10 (thanks Agarwaen!).
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.
First Strike - Unit always attacks first - I would prefer them to not shoot back at all.
Flag Killer - +5 attack when attacking enemy flags - infantry best friend.
Ignores ZOC - Ignores zone of control (ZOC) projected by enemy units when moving - sweet mobility add-on to any vehicle.
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.
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.
Precision Weapon - +20% base accuracy - great, but gets less impactful as experience grows.
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.
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.
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.
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.
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 - situationaly useful, does not hurt to have them in a unit
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.
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...
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.
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.
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.
Double Move - Units gets 2 move actions per turn, without increasing the number of movement points. - good for tanks as it help reach targets otherwise blocked or exploit formations. However, this should already be the role of Recons most of the time.
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.
Expert Recon - Provides 3x accuracy bonus on adjacent enemy units - not tested, however the bonus seems a bit overkill.
Expert Support - +20% accuracy when providing support fire - quite a large bonus, can see the crippling potential on high power support units.
Fast Learner - 2x faster experience growth - there are units such as fighters 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.
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.
First Aid - Restores one point of strength every turn the unit did not attack. Applies to infantry. - same as Field Repairs, but arguably better, since infantry is more prone to damage.
Fierce Fighter - +1 attack for each adjacent enemy unit - requires some foresight in unit placement, but can nicely add up.
Leadership - +1 initiative to all adjacent friendly units - will come into action often, but with a tiny benefit.
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.
Overwhelming Attack - Any damage to enemy units is enough to force the to retreat. - seems great, but can sometimes be liability more than a benefit.
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
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.
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. Might work nicely on overstrengthened units and... armored trains that attack as a single unit regardless of damage.
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 is not that amazing, but this has potential in an allied campaign.
Ignore Mass Attack - Immunity to Mass Attack - will come in handy once in a blue moon.
No Retreat - Unit never retreats - can sometimes help hold the front line, but rare to mater at all.
Prudent - Gets defense bonus for each point of lost strength - meh. There are some tricks to that, but did not find this too impact anything much so far.
Readiness - Strikes first when defending - seems like only a thing on low defense high attack AT units (Marders for example)
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.
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.
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.

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, but I prefer permanent bonuses.
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...
Fast Retreat - +2 movement points when unit's strength is 33% from maximum - just no.
Ferocious Defense - Entrenchment of this unit cannot be ignored - how often do you realistically expect to defend against AI pioneers?
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.
No Surrender - Unit never surrenders - it's much better to just avoid positioning units badly.
Safe Transit - Takes only 50% damage when caught in organic transport - or it's easier to just escort transports properly.
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
Consolidator - Can consolidate more than normal strength into a single unit, thus increasing maximum overstrength which the unit can have by +5 - so far I always took No Overstrength trait anyway, so...
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.
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.
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