The first edition of Warhammer 40000 (called "Rogue Trader") wasn't meant to be a competitive, tournament game, but more like a skirmish game with RPG elements. So it's not really surprising that it was possible to create hideously unbalanced units. Perhaps the most notorious example is a squad of Imperial Guardsmen (essentially the cannon fodder of the game) armed with grenade launchers firing Vortex Grenades. Sure, the grenades were expensive, but that one squad could basically lay down a set of ten templates that would instantly destroy any enemy they touched. To make it worse, in the first edition a squad was allowed to split its fire between several targets...
Second Edition had its share, some of which were errata'd out in White Dwarf. For example, Wolf Guard Terminators were said to be able to take any combination of weapons and could be built from stock parts with an Assault Cannon and Cyclone Missile Launcher [back in the days when you could essentially alpha strike with every rocket in the launcher; White Dwarf said if such a deadly squad actually existed it would have been included in the fluff text], the Imperial Assassin could in theory be disguised as a Gretchin while wearing Terminator Armour and riding a bike [removed when the Polymorphine Wargear was made specific to Callidus Assassins] and the Strategy Card 'Virus Outbreak' could cripple an entire Ork or Imperial Guard army before a battle even started [the official line was that players should destroy their copy of the card].
A lot of Second Edition special characters were also so powerful the game would end up revolving around them; many of the Third Edition changes were designed specifically to play down the monstrously complex special rules and wargear posessed by such characters.
One of the most overpowered units in Second Edition was the Eldar Guardian (basically Space Elf militia). While their stats were actually rather poor, they were also quite cheap and could carry Shuriken Catapults as standard weapons. So what's so bad about that? Well, before it was toned town in the next edition, the Shuriken Catapult was just insanely powerful for its price (even the Power Armour of the Space Marines offered little protection against it). So a single Guardian with a Shuriken Catapult wasn't that big a deal. But they were so cheap an Eldar player could spam huge numbers of them and slaughter his enemy's infantry by the dozens.
Second Edition Tyranids didn't use the strategy card system and instead got a ludicrously overpowered replacement; the Tyranid player could roll for every squad, character and vehicle in the opposing army and inflict annoying or game-screwing effects on a large portion of the enemy army before the battle even started. Results included a squad member randomly becoming a Barbed Strangler blast, and a "Lurker" creature being placed inside an enemy vehicle that would attack the crew if it moved. They also got two special mission cards that instantly nullified their opponent's mission, and one ("Tyranid Attack") also gave them infinite reinforcements and two extra turns.
There was also a chronically unbalanced Nid psychic power called "Psychic Scream" which allowed them to attack every enemy Psyker at once and forced them to roll 2D6; if they rolled over their toughness (likely) they wouldn't be able to do anything that Psychic Phase, and if they rolled over their Leadership they instantly died. It seldom took that long for the Nids to kill every enemy Psyker this way. This was nerfed in later editions.
The second 3rd Edition (3.5 ed) Chaos Codex was a one of the most overpowered codices, with multipleGame Breakers:
Iron Warriors could take up to nine Obliterators for elites and four Heavy Support choices, one of which could be a Basilisk, instead of the usual 3 for both. Take an already tough army, and back them up with nine plasma cannons, an earthshaker cannon, and three battle cannons? Any army would have difficulty not being wiped off the board.
Next up was the notorious Siren Prince/Lord. It was a Daemon Prince or Chaos Lord with a jump pack/wings/bike (anything to make him faster) who had the "minor" psychic power "Siren". That power made the enemy unable to attack him with shooting for one turn. The Prince/Lord would then proceed to zoom forward and summon a horde of Daemons/Chaos Terminators right in the middle of the enemy army. The only catches were that the power was one of six results you could roll up when you paid the points for a minor psychic power (though the risk could be reduced by paying for several rolls on the table) and that it could be countered by some enemy characters (but not all armies had characters who could do this).
Generally, lots of units were more effective than they had any right to be due to the veteran’s skills and daemonic gifts available to the whole army. Tank hunters made Havoc’s firepower far more brutal than anything anyone else had. Infiltrate popped up on many units, notably Raptors allowing first turn charge and melta tank popping. Sergeants were stronger and with more attacks than any other squad leaders. Daemon Princes were only limited by your imagination in terms of power.
Obliterators and Daemon Princes were in general extremely broken, the first one so much so that they had to release an errated version of the Chaos Codex specifically to nerf the Obliterator (reducing his base strength and toughness so that he could be insta-gibbed by a krak missile, and so that his power fist got less of a bonus). Even then, the Obliterator still got a stat nerf in the new codex, having completely lost it's strength and toughness bonus and half his weapons, while remaining at the same cost. Daemon Princes, likewise, lost nearly all of their options, with many more being severely restricted (especially since they are no longer allowed to carry daemon weapons).
There was also the infamous Dreadaxe+Daemonic Stature+Daemonic Strength combo, which allowed the player to create a relatively inexpensive model that dealt out 5 (6 on the charge) strength 6 attacks that ignored all saves. Add Daemonic Flight, and boof: instant Hero Killer.
The Third Edition Eldar Codex: Craftworlds was not quite as bad, but it was up there.
The Biel-Tan list allowed you to take any infantry Aspect Warriors as Troops choices. Not scared yet? When thirty Dark Reapers are ramming their sixty Strength 5 AP 3 missiles with 48" range and a two in three chance of hitting down your troops' throats, you will be.
Ulthwe replaced the standard Farseer and Warlock choices with the Seer Council, a squad of 2-5 Farseers and an infinite amount of warlocks. Warlocks also got a new power Augment, allowing them to double the Farseer's range. This, coupled with the fact that any Ulthwe Compulsory Choice Guardian Squad were automatically upgraded to Black Guardians (which had improved Ballistic skill or Improved Weapons skill depending on their profession)for free made Ulthwe armies a force to be reckoned with.
The Imperial Armored Company list (thankfully no longer legal) had Leman Russ battle tanks (around the fourth toughest tank in the game after Monoliths, Land Raiders, and Falcons) or artillery for every slot in your army.
Quite probably the single most overpowered army of 3rd Edition however was the Blood Angels. For starters, they got every benefit standard Space Marines got with none of the downsides, and often for fewer points. However, the real craziness involved the Death Company, who were totally insane superpowered combat beasts... which were also free, instead coming with other rather insignificant restrictions. The real bullshit however came from the fact that Blood Angels had Rhinos which were of the Fast type, making them significantly faster than normal Rhinos and gave them the ability to Turboboost. This meant that they could move 36", or 3/4s the length of the board from deployment edge to deployment edge, in a single movement phase. As third edition had no limitations regarding the ability to assault out of vehicles... suffice it to say that the Blood Angels codex was feared and hated for a while.
Eldar Falcons (basically fast anti-grav tanks with decent firepower that could also transport a small squad) were considered the cheesiest unit in the game, since they were almost impossible to destroy as long as they kept moving, due to their holo-fields allowing them to re-roll on the vehicle damage table and gaining a 4+ save for moving a small distance. As an illustration, a lascannon (one of the most powerful anti-tank weapons in the game) shot had a 1.2% chance of destroying it. Yes, that's one point two, not twelve. This, along with Harlequin payloads who due to the ‘’rending’’ rule would obliterate most squads they assaulted, meant an Eldar army was incredibly hard to stop, let alone damage.
The Eldar also had the ability to take an entire army on Jetbikes, led by a Seer Council, which was frightfully powerful at both range and assault, as well as almost impossible to hit.
Daemonhunters have several abilities designed to combat daemons. One of them is Sanctuary, which creates a bubble around the caster that no daemon can shoot, move, or see through. While the caster of the ability can't shot or assault, nothing prevents other units inside from doing so. Back when Daemons were a unit type in Chaos Space Marine army this wasn't a major problem, as the marines could still get through the Sanctuary. However after Daemons were given their own codex, dropping Sanctuary on objectives or on some psycannon-toting purgation squad makes the game unwinnable for the daemon army. Furthermore, as Daemonhunters can be allied with any Imperial force, any Imperial army can take a cheap Daemonhunter Inquisitor to completely screw over any daemon armies thay face. This lasted until Grey Knights were given a new codex in 5th. See below though, as Daemons' problems didn’t end there…
The 4th edition Ork was widely considered one of the most overpowered codices Games Workshop has ever produced, and is notable for remaining fairly competitive and winning tournaments from just after it was released at the end of 4th right up until the end of 5th. Many of the units were under-costed (at the time) for what they do.
The worst offender was the now infamous Nob Biker army, an army that uses Warbosses to count Nobs as troops, then place them on bikes, and give each model different equipment for the sole purposes of exploiting the new wound allocation rules. This gives Ork players a loophole by which they can place wounds on individual models to prevent casualties from being inflicted (you're normally supposed to place wounds to inflict casualties first). On top of that, Nob Bikers have 2 wounds each being on bikers an extra toughness point, always count as being in cover (which gives them a save they can always take), and odds are you're going to give them cybork bodies (another save) and a pain boy (yet another save).
A standard Ork Boy is essentially a mini-Khorne Berzerker for the cost of a Guardsman, one of the weakest units in the game.
Burna-Wagon: 1 Battlewagon, 1 Big Mek with Kustom Forcefield and Burna, 15 Burna boyz. With the forcefield counterbalancing the speed limit required to fire, Exploiting the open-topped transport rules allowed the squad to stack 16 flame templates on top of each other, eg: If 2 space marines are under the flame template, then the squad receives 32 hits (2 x 16), or for example 8 Gaunts from a squad of 32, results in 128 hits (16 x 8), which should remove the existence of any squad, barring certain bizarre circumstances brought on by the Random Number God.
The Big Mek and his Kustom Force-Field. This rule was made in the 4th edition, where the rules for Obscured Vehicles was slightly different and less forgiving to vehicles in general. It's reflected on infantry by only giving them a 5+ cover save (barely usable). In 5th Edition however, this resulted in every vehicle essentially ignoring half the shots coming at them. The infamous "Killa-kan" lists exploited the fact that you only needed one Killa-kan in the squad to be within range of the Big Mek to have this benefit, while running around with what amounts to 9 space marine dreadnoughts tearing up the enemy forces. Bear in mind most units cannot even harm a Kan without grenades, let alone survive the inevitable onslaught.
Chaos, though much less than before. Though funnily enough it is another psychic power from Slaanesh causing problems. 'Lash of Submission' allowed players to move an opponents models up to 2D6 inches, meaning you could be moved of objectives, lured into position for a first turn charge or clumped together to make most of the multiple blast weapons.
Tau's "Fish of Fury". Two Devilfish transports could form a mobile bunker for their Fire Warrior cargo. While armies with a good amount of anti-tank ranged weaponry had a somewhat easier time taking the Fish out, assault-heavy armies (which were supposed to be Tau's soft counter) were pretty much boned because the Fish were almost 100% assault-proof (and thus, so were the deadly riflemen behind the Fish). The tactic was so abused left and right that many Tau players would actively decry and avoid using it. The change to skimmer rules in 5th edition that allowed skimmers to be attacked in assault finally allowed assault armies to stand a chance against the Fish, And There Was Much Rejoicing.
The 5th edition Imperial Guard codex has a psyker battle squad with an ability that can be used to drop the leadership of one enemy unit by the number of psykers in the squad (to a minimum of 2). This already is nasty enough, but combined with a Callidus Assassin from the Inquisition codexes (which can be taken as allies) is becomes a real Game Breaker. The Callidus has a template weapon that deals damage based on leadership, so by combining the two you get a flamethrower that wounds on 2+ and instakills anything without a special rule that makes it immune to instant death. Oh, and the assassin will automatically appear near an enemy squad so it'll always get at least one shot in. On the plus side, this is probably the best way to deal with the aforementioned Nob Bikers.
Perhaps even more game breaking are "Meltavets", veteran squads (which were made troops in 5th edition) in a chimera and armed with 3 meltaguns, allowing them to fire 3 meltagun shots from relative safety in their metal box for pretty cheap. If you were one to prefer a faster firing option, for 125 points you can field the same squad except with 3 plasma guns and a plasma pistol instead of 3 meltaguns, allowing you 7 shots that can chew through marines, terminators, and light vehicles with ease. This was in an era where large amounts of armour reigned supreme.
There was also an infamous combination of 5th Edn IG with 3rd Edition Daemonhunters (they don't get updates often) rules, which involved copious amounts of Tank Goodness and psykers. It swept every army off the table at 'Ard Boyz within an hour. The only list that could come close to countering it was a flying Seer Council Eldar list, created as a fluff-based Army, which only worked against it. It was named, because it swept away enemies like leaves, the leafblower list. It died off because "It's Popular, Now It Sucks" is played straight in a tournament setting - once people see something more and more, they figure out how to stop it.
The entire Grey Knights codex (created by Matt Ward) has been called this, due to insanely powerful units it contains:
Dread Knights, Standard marines in a walker, basically a faster and cheaper version of dreadnoughts before they were reconsidered as vehicles.
Terminators and Strike Squads, the most basic troops available. All have storm bolters, force weapons and psychic powers for +1 strength. Meaning for the same price or only 5pts more each respectively, these units vastly overshadowed ordinary marines and spelt death to light infantry and monstrous creatures alike, although this problem was present in the previous codex.
Paladins, two wound terminators who used the same wargear shenanigans to abuse the wound allocation rules to recreate the Nob Biker style unit, only trading speed for tremendous firepower, better close combat ability and increased resilience. These might have fallen out of fashion like the Nobs had it not been for…
'Psyriflemen', Dreadnoughts with 2 Twin-linked autocannons with psybolt ammunition. This was the most reliable long range low-mid armour buster in the game, meaning the grey knights in fact had no real weaknesses. It wasn't helped by the fact that the current meta meant that large numbers of light tanks where in almost every army at the time.
And just in case being generally overpowered wasn’t enough for Daemons to deal with, Grey Knights have a whole bunch of pain just for their immortal foes. Worst of all is the psychic powers ‘Warp Quake’ all the basic troops can use. Essentially, it makes deep striking near them a death sentence. Did we mention Daemons have to enter the game by deep strike?
Plasma Siphons. Plasma weapons are the most reliable way to get through a Grey Knight's armor. Plasma Siphons make those same plasma weapons nigh useless. It has the same effect on Pulse weapons, which are standard issue weapons for the Tau (a faction based entirely around ranged firepower) and are used by practically their entire army.
The 5th edition Necron codex (also created by Matt Ward) can be considered a Reconstruction of the Game Breaker trope. Necrons are incredibly powerful on midrange (24 inch and less) with almost multiplying attacks (Tesla guns) and very resilient, coming back from deadness every phase (not turn, PHASE) unless they mess up, but in turn are very slow unless in transports. Problem is that unlike say Tyranids nearly every problem in the official FAQ relating to them got solved in their favour, making many suspicious situations even worse when facing them. Which is the whole point, because according to the fluff they are supposed to be literally unstoppable in the long run.
The Space Wolf Rune Priest has no less than three very powerful psychic abilities: Murderous Hurricane harms a unit and makes all terrain difficult and dangerous for it, Living Lightning is an unlimited-range S7 shot, and Jaws of the World Wolf has a guaranteed 1/6 chance of killing any nonvehicle model.
To add to this, Space Wolves can take up to FOUR HQ choices.
In fifth edition it was virtually impossible to not field an overpowered Space Wolves force, simply because the cheese extends to the basic Grey Hunter, which is both cheaper than a Tactical Marine, while being capable of everything the Tactical Marine can do, and more.
Blood Angels (again, written by Matt Ward, see a pattern?) are an amazingly overpowered army. EVERY vehicle, save the Storm Raven and Land Raider are Fast, they can Deep Strike Land Raiders, can take Dreadnoughts as Troops (which means that they can take an ELEVEN Dreadnought list), among other cheese. Many fans feel that the three strongest Fifth Edition codices were Necrons, Grey Knights and Blood Angels for a reason.
It's still a bit early to draw the Game Breaker line for 6th Edition, but for the moment Flyers have this title. They're fast vehicles who are almost impossible to hit with traditional anti-vehicle weapons like Krak Missiles. Unlike Fast Skimmers, the previous Game Breaker, Flyers can't be assaulted at all, meaning your expensive Thunder Hammers and Melta Bombs are completely uselessnote actually, that's a lot like Fast Skimmers, the previous Game Breaker. The only units who can reliably damage Flyers are models with the Skyfire rule... and the only models with the Skyfire rule by defaultnote at time of writing are other Flyers and a single Imperial Guard vehicle. This will (presumably) be a self-solving problem as more factions get updated army lists and new fliers and counter-flier units of their own, but until that time those operating off an older list are at a disadvantage because they have nothing to engage the new rules with.
Admittedly, some of these lists were the result of players not fully understanding certain rules. That list has only 15 ground troops, only one of which is even in power armor, which meant there's a very, very good chance the entire ground force will be wiped out turn 1, causing the Grey Knight army to lose the game before the Stormravens can even show up (The game ends if one side has no models on the board at the end of the game turn, and fliers can't start arriving until turn 2). Of course, this didn't stop more balanced lists with several fliers supporting a decent ground force from ruining the day of those who failed to bring enough flier defense (or worse, played a codex without access to flier defense).
Imperial Guard has become insanely powerful in 6th for two reasons: it has one of the cheapest flyers in the game points-wise, which also happens to be one of the most durable, versatile and deadly: the Vendetta. It has the higher level of flyer armor, three twin-linked lascannons meaning it almost never misses and will smoke any tank/flyer/elite infantry easily, and it's also a transport. Did it fail to nuke the target? Well, the 10 veterans with meltaguns it just dropped close to the enemy will finish the job. Adding, insult to injury, it can be squadroned, meaning you can bring up to NINE of them in a single FOC game. The other factor is the low point cost of almost everything in the codex, meaning that you can bring so much stuff to the table (stuff that usually just has -1BS compared to a much pricier and worse Marine equivalent) that you can bury the enemy in firepower and bodies. With the Allies system you can even bring in Space Marine special character to make blobs of dozens of guardsmen fearless and unstoppable.
In the same vein as above is the infamous "Cron Air" list: no fewer than nine flyers and a ground unit who, thanks to a quirk in the rules, is more or less literally invinciblenote what you do is take a "battalion" fortification and block the ground unit off in the corner; the enemy team isn't allowed to shoot at the ground unit (no line of sight), nor are they allowed to collapse the battalion as long as the ground unit doesn't actually enter the building.
"Scythewing," as Necron flier-spam was dubbed, got around the problem many armies faced when trying to spam fliers due to the fact it could also Spam large number of difficult to draw line of sight to Ground units through Scarabs and a unit of Canoptek Spyders.
Note that allowing Forge World units seems to alleviate flyer problems considerably since good AA options/flyers are plentiful for most armies should FW models be in play... Which is gradually becoming more common, but there are still some groups out there that are firmly convinced Forge World is inherently broken.
The 6th Edition Chaos Space Marine is generally considered to be relatively well balanced...with the notable exception of the Heldrake. In addition to the general difficulties many armies in early 6th edition have with fliers, the Heldrake is the only flier to have an invulnerable save, and is has the best front and side armor that a flier is allowed to have, making it the most durable flier in the game outside of Forge World supplements. It also had the "It Will Not Die" special rule, allowing it to regenerate hull points, meaning that even if you managed to damage it, there was no guarantee that it wouldn't be able to regenerate the hull point damage before you could shoot at it again. Further complicating matters was its ability to destroy light transports or slaughter infantry during the movement phase, before firing a weapon that could obliterate any infantry model without an invulnerable save or a 2+ armor save, bypassing cover saves. A FAQ ruling would only make matters worse, giving the Heldrake the ability to fire its weapon in a 360" arc—removing the positioning element that was its only real weakness prior to the FAQ.
The Battle Missions expansion features a special ork scenario which combined with the Apocalypse rules for force selection, take Ghazghkull and a few warpheadz you could have an ongoing Ghazghkull Waaagh!!! from turn 2 to the end of the game! It is countered by the point that Apoc level lets you take Titans or Baneblades.
Ghazghkull Mag Uruk Thraka personified this trope throughout the editions. Currently it's because of his two-turn buff that makes all Ork infantry very mobile, and grants him the hardest defense to beat in the game (Rolling a 1 on a six sided dice, four times in a row), but only for two turns. The problem is that the average game is six turns.
One of the Tyranids' special formations in Apocalypse had a horribly broken rule called "Out of ammo, Sarge!" which was intended to reduce the effectiveness of shooting at it by discounting all shooting if more than six 6s are rolled. Its actual writing omitted the shooting part and used the word attacks meaning that in melee if more than six 6s were rolled the entire squad lost its ability to punch/slash/stab. This is horrible as most melee units will roll upwards of 20-30 dice. Considering this applies to a blob of 120 'Nids, it considerably unbalanced battles and GW took too long to correct the mistake which was glaringly obvious to any player who had experience with several codices.
Forge World's creations have been very overpowered in the past. The Elysian Drop Troops list in Imperial Armor volume 4 gave the Elysians the ability to take flying Valkyries as dedicated transports for every single squad. And flyers in this game are almost impossible to kill, as non-AA weapons only hit them on a 6 and all weapons have their range reduced by 12", and nobody in a normal-sized game has an AA weapon with a ghost of a chance of taking out a Valkyrie. Did we mention that they get Vultures (Valkyries that sacrifice transport capacity for more guns) as Heavy Support, and their flyers can mount three to five specialized heavy weapons each? No wonder these guys were so good at taking down Tyranids.
Forge World lists are explicitly only meant to be balanced with lists in the same book, they require opponent permission to use and are never tournament-legal, except in their own tournaments (after all, anyone who pays 960 GBP for a Tau Manta needs to take it out the box sometime).
Shortly before the 6th edition Chaos codex was released, we were treated to a White Dwarf update for Daemons. Aside from introducing the new Slaanesh chariots there were also new rules for some resculpted units. The most notable of these were the Flamers and Screamers:
Both units were now T4, with 2 wounds, a 5+ invulnerable save and the Eternal Warrior special rule, making them immune to instant death. At 23/25pts a model, this is insanely durable, requiring 9 bolter shots to kill a single model in an army where the maximum of 54 of these guys can happily be fielded. This might have still been ok, had this not been combined with how powerful both units where.
GW is trying to tone down players abusing the broken armies by stating that the "Most Important Rule" is to have fun, not to win. Generally Store Managers and a good deal of players look down upon "power gamers", players who play only to win by exploitation. However, to move their products, they inevitably make a few lists composed of the most expensive models, which only exacerbate the situation.