World of Warcraft has had a number of them, mostly in PvP content. However there have been a few PvE ones. Zul'Aman was also famous for creative ways to use certain skills to subvert major parts of the dungeon's challenges; pulling enemies using pets to get past walls, preventing them from summoning Goddamned Bats, certainly helped, but when the challenge of one boss is that it is a 5-man team, and you could (now fixed) literally make all but the "leader" despawn using a creative trick involving a frost trap and a naked blood elf.
For a while there was the "Reckoning Bomb", which gave an extra attack on the next swing after getting critted, and could stack infinitely. That is to say, a paladin could spend a few hours doing nothing but standing in one spot getting hit, then go ahead and hit a raid boss. All the Reckoning charges would be emptied out instantly, giving the Paladin thousands of extra attacks in one hit, killing the boss on the spot. Needless to say, the nerfbat was quick in the coming.
The Paladin's old Horde Counterpart had a far worse version in their "Windfury" ability, which gave each of their autoattacks a chance to attack again. This orginally could proc off itself, leading to infinite attack loops. Unlike the above mentioned "Reckoning Bomb" Windfury instant gibbing players could happen off sheer random chance.
A different kind of Game Breaker back at release was the fact that you could kill enemy flight path masters, which just shut down transportation. Blizzard allowed this, but punished people who did this by automatically giving them hated reputation with their own faction, so your own faction NPCs will be hostile and attack you, making it virtually impossible to quest, shop, etc. on that character. They realized how stupid this idea was when some rogues began killing enemy flight path masters, then snuck back into their own faction cities and killed their own bankers, auction house masters, flight path masters, quest masters, etc.
In a similar case, there are quests you have to turn in to your faction leader (ie. King Varian Wrynn). However he can be killed, and has a six hour respawn time. So if you're a new Death knight, TOO BAD.
On the PvP front rogues at one point enjoyed the possibility of "stunlocks" in Player Versus Player, which meant they could use their various stunning/disabling skills to make an enemy completely unable to defend themselves for an unlimited amount of time. This was counteracted by so-called Diminishing Returns in PvP, which make such abilities less and less effective the more they are used against the same opponent in a certain timeframe, as well as special PvP equipment that allows players to break free of one such effect every few minutes.
The infamous 'World of Roguecraft' series of videos featured a player using stun locks along with the Eviscerate move which at the time did static damage no matter what the user's attack stats were to kill players while naked.
And wielding a Worn Dagger, which has a DPS of less than one.
For a long time after the game was released (nerfed now, thankfully), Night Elf Hunters could charge up an Aimed Shot while invisible by using Shadow Meld. With decent gear, an Aimed Shot crit could almost kill a cloth wearer in one hit.
Although currently eliminated from the PvP metagame, a common PvP Priest build used to involve acquiring as much armor as possible, leading to a damage reduction similar to mail and a shield, rendering them nigh unkillable healers. Paladins, who have even more armor and defensive abilities, also had their moments of glory.
Lets not forget Warrior during the heyday of season 3 arena. Plate Wearing juggernauts that can take off a quarter of your life on a crit (that's if you were also in plate, god help you if you were in leather or cloth) while reducing any healing you get by half. If you try to slow or snare them they will fly across the field at you, if you try to stun them they will actually heal themselves. There was a reason 9/10 of the top 2v2 teams were Warrior/x.
In classic vanilla, Warlocks were often considered underpowered and and quite weak in PvP, and was often only brought along for specific PvE encounters. Cue the buff to Death Coil, making it an instant fear, heal and nuke on a relatively short CD, massive buffs to talent trees and the introduction of better +damage gear skyrocketing the DPS output of DoTS and Warlock nukes. Suddenly a single Affliction Warlock could have DoTS doing 4000+ damage in battlegrounds, usually far more than the average health pools of anything but tanky Warriors or Paladins in the day, and even the ROGUES were complaining that Death Coil, slows and instant fears basically made Warlocks invulnerable in 1v1.
Warlock difficulty did not end in 1.8, regardless of what the screaming, whining general populace of the time, with their constant and incessant NERF LOCKS NERF DEATHCOIL rantings would have you believe. An incredibly popular Add On of the time, 'Decursive', permitted Priests and paladins to automatically dispell any harmful effect on any friendly player within range, without having to first target that player - or ever even knowing that that player needed dispelling. All Warlock (and Shadow Priest) DPS at the time came from DoTs, a single Paladin spamming their Decursive button could easily render any Warlock (ot Shadow priest) wholly irrelevant. Subsequent fixes deliberately broke Decursive and in the first xpac, The Burning Crusade, Warlocks received a new DoT called Unstable Affliction, which detonated in the dispeller's face if cleansed, causing massive damage and a 5-second silence. It must be noted that the early part of TBC, UA warlocks were nigh-unstoppable killing machines, inarguably 'overpowered' and unbelievably fun - especially after all that time of being everybody's free HK.
Even Druids had their moments. Restoration Druids were the undisputed kings of PvP healing for a while thanks to Lifebloom, a very effective instant cast that heals over time and even if the opponent could dispel it, it would only heal more . They also have a very useful spell in Cyclone, which doesn't last as long as other control spells, but is nearly impossible to break.
Not only Lifebloom, but with the introduction of the Arena, Druidic healing became much more useful, simply because it was so focused on heal-over-time spells with no (Lifebloom, Rejuvenation) or short (Regrowth, Nourish) cast time. While these skills were weak in other PvP environments, in the arena the ability to cast some healing without staying still long enough to get focus-fired by your opponents was invaluable.
Early Wrath Starfall gave Moonkins the very useful (but unintended) ability to break enemy Rogues out of stealth in a huge area, along with a chance to stun. It didn't last long however, and the spell became very underwhelming without these traits.
Something similar happened with the Death Knight spell Blood Boil, which hits everything in a 10-yard radius around the Death Knight. When the class was first introduced, the ability would fail to cast if there were no targets in range. Players quickly realized this meant they could spam the button if they suspected a stealthed Rogue or Druid was nearby, and it would hit them and knock them out of stealth the second they came within range. Blizzard eventually changed this so that Blood Boil will cast (and consume Runes, making it non-spammable) regardless of whether it hits anything, but will only generate Runic Power if it does.
Feral Druids had their moment early in Cataclysm. They could load up an enemy with bleed effects For Massive Damage, then pop into Bear Form and become nigh unkillable.
Patch 2.4 and 3.0, before Wrath was released to the mainstream public, gave Paladins level 80 abilities and damage at level 70. This patch was known as "Wrath of the Retadin". This was considered blasphemy to many other players, and it wasn't uncommon to see a battleground 3/4 or more full of Paladins. (Prior to this time, Retribution-build Paladins were considered leveling only builds, useless in Endgame Raids unless they respec'd as healers or tanks.) Although the developers intended to make Inscription and the level 80 skills available to players and for the game to balance out as the characters were leveled, the outrage and forum outcry was enough that Blizzard took the nerfbat to Paladins in 3.0.2 - making them vastly underpowered even compared with before. Retribution-build Paladins weren't fixed until the Secrets of Ulduar patch rebalanced the skills of every class.
To put this in perspective - a Season 2 Geared Paladin could walk into the middle of a group of cloth and leather wearers in PVP with Seal of the Crusader on, do a Consecrate and Divine Storm, and kill or severely hurt anyone in a close proximity who were hostile. T6 geared paladins could solo a heroic instance at level 70 - something hard to do for even all but the most heavily geared 80s at this point.
Paladins were called as primary targets for months after the patch was fixed on Battlegrounds.
As a matter of fact, whenever Blizzard introduces a new spell, it is guaranteed that it will be either unanimously considered useless, or someone somewhere will call it a Game Breaker. The balance of WoW is to avoid having any one class staying a Game Breaker for too long.
For a very short period in patch 3.3, Fire Mages had an unintended effect in one of their talents (Pyroblast can be cast instantly with two consecutive critical hits, at a cost of 0 mana) that caused their primary nuke spell (which normally has a long, 5-second time to cast) to be available as an instant-cast more often that intended, leading to the possibility of a situation where the Mage can repeated spam this high-damage ability for significant burst damage. As a result, a hotfix was quickly released to prevent damage-over-time-critical-hits from counting towards consecutive critical hits.
According to some people, the new Tol Barad PvP zone is grossly imbalanced in favor of the defending force. Let's do the rundown: The goal of the zone is to capture three fortifications: Wardens Vigil (southwest), Ironclad Garrison (north) and Slagworks (southeast). These are placed in a triangular formation, with the defending respawn point in the middle of them all. To cap a fortifications flag, you need to have more people on it than the opposing faction. Here's the problems:
In order to cap the flags, the attackers need to outnumber the defenders. Fair enough, except to win the attackers need to cap all three forts at the same time. If the defenders hold just one, they win.
The attackers respawn right outside the closest fort they're trying to cap, whereas the defenders respawn between the three forts. While this means that the attackers have a shorter distance to each individual flag, the defenders can swarm any undefended flag left unguarded by the attackers, retaking it in a matter of seconds while the attackers are still moving towards the next flag.
This will inevitably result in the attackers rushing around the zone, trying to cap all three flags, while the defenders zerg whichever flag has been left unguarded.
Blizzard has since done a lot towards fixing the blatant nigh-impossibility of an Offensive win, mostly by altering how fast the keeps convert - the more forts capped, the faster they covert, meaning once you already have 2 forts, the third caps incredibly fast, forcing the defensive force to move fast to keep in the game. Tol Barad is now at least as reasonable as Wintergrasp. (Whether or not Wintergrasp is reasonable is something entirely different.)
Death Knights are arguably this when tanking. Mitigation on par with other tanks, passive group heals that are at the very least on par with Shadow Priests and Retribution Paladins, damage easily comparable with a DPS, one of the best group buffs in the game, and almost as many defensive cooldowns as all the other tanking classes combined.
And now the latest game breaker, Beast Mastery hunters due to one, incredibly broken skill. Stampede which summons out 6 pets for the hunter and increases their damage by 75%. Note that a hunter's pet does half of its damage. This has lead to hunters killing other players in less than 2 seconds.
The math for this? 175x6x0.5 (how much the pet is doing x how many pets x % of the hunter's damage) is 525% damage.
Not content to only give them one overpowered ability, Blizzard gave monks both Touch of Karma and Ring of Peace Touch of Karma makes someone take all their outgoing damage instead of the monk, while the monk is free to whale on them, Ring of Peace completely renders everyone near a monk's chosen target helpless while getting wailed on.
At the start of Mists of Pandaria, Holy Shock, a spell for Holy Paladins was made this. It dealt incredible amounts of damage and in PVP, could easily take off 60-90% of a target's health, if not one-shotting them outright. Its damage output was cut by a full 60% later, but for a while it was a bloodbath.