Yu-Gi-Oh!: Noah's deck master Shinato's Ark is this all the way. First, whenever an opponent attacks Noah directly, he gets to special summon a monster in the Graveyard to block the attack, and can do this once for each monster in the Graveyard. Second, he can outright remove all the monsters in both Graveyards from play to gain 500 Life Points for each one. And then when the Ark is destroyed, Shinato itself is summoned. Whenever Shinato destroys a monster, the opponent's Life Points are cut in half and Noah's points increase by the same amount. When the opponent takes battle damage, Noah gains the same amount of points they lost. Whenever Shinato would be destroyed it moves back off the field into the Deck Master position, so it effectively cannot be destroyed. Oh, and it has 3300 ATK points. No wonder Noah became the first duelist in the show to get over 10,000 Life Points.
Yugi is only able to defeat it by getting his Obnoxious Celtic Guardian (which can't be destroyed by any monster with higher than 1900 ATK points) on the field to soak up damage for a bit, then tricking Noah into attacking a facedown Cyber Jar that removes all monsters on the field from play (though Shinato has yet another a special ability that lets Noah stay in the duel despite its destruction, and still use its abilities). To make a long story short, Yugi then gets Blue-Eyes Ultimate Dragon on the field, attacks, uses De-Fusion to summon the 3 Blue-Eyes White Dragons, then attacks with all three of them, hitting Noah for a total of 10,000 damage points.
JoJo's Bizarre AdventureGiorno Giovanna's final stand, Gold Experience Requiem, is a literal example of this. With this stand no action, process, ability, ANYTHING, can cause Giorno harm, nowhere, nohow, even defying time and space to protect itself and it's user. Nothing can touch him, and the consequences for being killed by it are even WORSE.
Mahou Sensei Negima! does a Shout-Out to this concept with Jack Rakan, who's so absurdly powerful that the other characters start referring to him as broken.
Chisame: This guy is so broken it's not even funny!
In a similar instance to Jack Rakan, Priscilla from Claymore is broken enough that she can probably thrash an Eldritch Abomination among Eldritch Abominations. Against regular enemies, she even states she finds it difficult to go easy enough to avoid killing them.
Aizen Sousuke from Bleach is referred to as "Captain Broken" by fans thanks to his absolutely ridiculous ability to completely control the senses of anyone who sees him release his sword even once. And that's one of his low-level abilities. And, of course, he also managed to block the hero's most powerful attack with one finger.
He also manages to damn near kill a fellow captain using a high-power hado (destructive art) without performing the full incantation, which means that the technique was 1/3 its normal strength.
Yamamoto possesses the most powerful Zanpakuto in existence, Ryujin Jakka. It is so powerful that Aizen opted to use a Modified Arrancar to seal it rather than face it directly. Its Bankai, Zanka no Tachi? It is so powerful that just by existing it threatens to destroy the world if it is released for too long. "Reduce all creation to ashes" indeed.
And even that has it's weakness, being that it inverses the standard rule of Logia types - instead of being able to dodge all attacks (excluding maybe one polar-opposite element), he can't dodge anything.
Drowtales - The fae, especially the drowolath/drowussu/vanir (light elves). Drowtales is not a setting that is aimed to be balanced in terms of power between factions and species. Period. The humanoid fae are not only dominant in terms of power compared to other species who can't use mana, they are also unbalanced (in terms of gaming) within their own species. It is mentioned in the immortality podcast that very old dokkalfar or drow can reach a point where they are so powerful that they could literally wipe out a small army (drow size army, granted) of 'normal'/young (60-200 y.o.) fae. Waes'oloth, the Beldrobbaen Ill'haress is the example used. Of course, by that time their aura has grown so huge/dense that they literally need a whole clan or even city to sustain their bodies in a prime condition. This is why Diva's 'ordinary' mana blast blew an entire mutlistory building down. Within the city of Chel she had sufficient mana to fuel her attacks to nearly godlike power levels. This disparity in power, both in relation to other species and within their own species, is what makes the fae dominant. Only their comparative absence from the surface for a millenia has allowed the goblin races (halmes, kotorcs, ferals, naga) to become dominant there. A dominance that can be wiped away if the fae (drow or vanir in this case) makes a concentrated effort to do so. (Luckily for the goblins, so far they seem to prefer trade and limited raids.) It is not balanced, it is not fair and it might rub people the wrong way but it is the fait accompli in the Drowtales setting.
In the Kidou Tenshi Angelic Layer manga, Blanche's Hyper Mode is considered a Game Breaker. Oddly enough, she's allowed to compete in national Angelic Layer tournaments and use the ability, and the game's creator is not enraged, but rather, fascinated by it.
In the parodic Let's PlaySonic the Hedgehog 2: Special Edition, playing as Knuckles the Echidna makes any level a cakewalk. In addition to gliding and climbing walls, he can jump really high (as in, high enough skip entire levels in a single bound or to almost leave Mobius' atmosphere) and he can summon artillery support to take out Robotnik in a single shot.
In Mythic Quest, the main character's Shadow Sword is so powerful it is often accused of being a hack in that video game by other characters. All the Shadow Spells fall under this, usually ending up in one hit KO territory.
Sports are not immune from their own game breakers. In baseball, the bunt used to be a game breaker as it allowed a hitter to take as many pitches as he wanted, able to stand there and bunt off every pitch until he saw one that he wanted to hit. As a result, the rules were changed so that a bunt foul with two strikes would count as a strike out, preventing the bunt from being abused.
Another famous baseball game breaker: since a batter's strike zone is dependent on his height, you might have wondered "so why don't they just send little people to hit?" In 1951, the St. Louis Browns (now Baltimore Orioles) did just that; they signed a little person to a contract and sent him to hit, and when he was (naturally) walked, removed him for a pinch runner. When the commissioner's office found out, they promptly invalidated the contract and mandated that all contracts in the future be approved by the league. No word on whether or not the Browns (one of the worst teams in baseball in this era) planned to play a team of nine little people and therefore score a theoretically infinite number of runs.
Basketball used to have a game breaker of its own. It used to be possible to get a lead in the game, then literally sit on the ball, forcing the other team to foul, hoping that the player would miss the free throws in order to get the ball back and have a chance of scoring. To solve this problem, Danny Biasone created the shot clock, requiring a team to take a shot within 24 seconds or lose possession of the ball. This addition radically changed the way that game was played, making old versions of the game almost unrecognizable today.
In (American) Football, the "Flying Wedge" is a very effective formation that tends to result in a lot of injuries, which is why it's been banned.
At the 1979 U.S. Open golf tournament Lon Hinkle was waiting at the eighth tee when he noticed an alternate route to the hole - hitting the ball through an opening in some trees and landing on the 17th fairway. He then shot from there to the green on 8 and birdied the hole. After the golfer he was paired with, Chi Chi Rodriguez, took the same route, USGA officials planted a tree overnight to block that approach. It's believed to be the only time a course in a major event ever had such an obstacle added during the competition. The tree is now known as the "Hinkle tree."
Subverted in Magi-Nation. A power gem could be bought for 8 animite and sold for 12 animite. However, while animite is the currency of the realm, you never need to buy items, as you can recover health naturally, and you need infused animite anyways to forge rings. Basically, its a game breaker in the most technical sense that you need animite, but you don't need it that badly.
Future GPX Cyber Formula: Hayato's Lifting Turn, in which, with v-Asurada AKF-0's effect fans, elevates the car and floats around the turn. It can also float around its opponents, giving Hayato tremendous advantage.
When Phineas and Ferb create a virtual reality game, Candace gets sucked in, with a Modesty Towel and more important to the trope a hairdryer reducing the use of "jumping and ducking."
The Mangekyo Sharingan and Rinnegan from Naruto can both be considered Game Breakers. Also recently shown Kabutomaru's use of Edo Tensei, which allows him to ressurrect an army of uber powerful zombies that can't be killed unless one summons a death god to rip the souls out of them. Unless you know them well enough to emotionally move them, or Kabuto hasn't put a special seal inside their head.
Similarly, the chakra-boost Naruto gets from the Nine-Tails that allows him to, eg, summon the toad boss. In fairness, he's usually fighting a gamebreaker enemy at the time...
It goes Up to Eleven in Biju Mode. Naruto has Bijudama now-which can literally wipe out islands and mountain ranges off the map. His speed is even faster than Nine-Tailed Chakra Mode. He can lift the 'Mini-Bijudama' in one hand and create Rasengans in one hand (when he wasn't able to do so before). His clones get all these attributes too, able to partially manifest Kurama or completely form him. He's the only character who made Madara get serious one-on-one.
As for Kabutomaru's Edo Tensei zombies, special mention goes to the real Uchiha Madara, who has both the sharingan and rinnegan, as well as the Shodai Hokage's Mokuton ability.
And The Juubi. It dwarfs both the Hachibi and Kyuubi in size, can move incredibly fast, is capable of both massive bijuudama/bijuu beams and can target anywhere on the continent. The only reason the United Shinobi Alliance isn't dead is because Madara and Obito want to break them psychologically.
How crazy is this series? Fiamma eventually gains power greater than that of God... and he's still only the fourth-most powerful character in the thing.
Darkseid has Omega Beams that cannot be avoided or survived. If he can see you, he can kill you, and there is nothing you can do about it. Naturally most of his defeats involve their effectiveness being massively downplayed, or he just flat-out forgets that he has them.
The spartan from Deadliest Warrior has a game breaker, in the form of his big ass shield. In both his fights, against a ninja, and a samurai respectively, he never has to do much besides let his enemy tire themselves out by fruitlessly whacking at his shield, then he'll move in for the kill.
In the video game, the Spartan also is a bit of game breaker, but for different reasons. His spear range attack flies at head level (and attacks to the head are almost always one hit kills), and can end a match within a second if the opponent doesn't move out of the way IMMEDIATELY.
In Mistborn the two primary magic systems are allomancy (where small pieces of particular metals are swallowed and then "burned" to grant particular superhuman powers) and feruchemy (where one can store up one's own attributes in pieces of metal and tap into them later- for example, becoming very weak and frail for a time lets you store the energy to gain Super Strength at a later time). For the most part, the two systems are Mutually Exclusive Magic- except for the Lord Ruler, who was both an allomancer and a feruchemist, meaning that he could swallow and burn metals in which he'd stored his own qualities, giving him access to insane amounts of power that no-one else in the series could match.
After the time of the original trilogy, full mistborn and feruchemists have become the stuff of legends while single-metal users of each have become more common. Occasionally someone is twinborn, with a single allomantic and single feruchemic power, though not always the same metals. One character in The Alloy of Law was twinborn to gold, meaning he could store health and then burn the charged gold for tenfold returns, creating a positive feedback loop of stored vitality limited only by his access to gold.
Alluded to in the title of PC gaming site Rock Paper Shotgun.
In ReBoot Bob's Glitch lets him be a cheating bastard in every game he's in. Then there was the one time he (mistakenly) brings a bomb into a racing game, and the explosion crashes the game. And the one time Matrix pulled out his Gun, in a Golf Game.
The NES version of Monopoly allows the player to make offers on AI players' property, which the AI will accept a certain percent of the time depending on how high the offer is. However, since there's no limit to how many times an offer can be made per turn, the player can repeatedly offer an extremely low amount for a property and the AI will eventually agree. Effectively, this means the player can take over the entire board with ease.
In an old version of PC Monopoly that came on a 5 1/2" floppy, the limited AI meant that a player who made an offer to an AI then had to turn the machine over to the other human players, who would then vote in place of the AI making a decision. Needless to say, in a single player game, this could be abused relentlessly.
In the Gundam franchise, the Turn A and Turn X completely overpower anything else in the series. Here's a partial list of their abilities: self-repair via nanomachines, teleportation, thrusters equal in strength to a battleship's, bending light to briefly turn invisible, I-fields that can even block kinetic weaponry, and, of course, the infamous "Moonlight Butterfly", which knocked Earth back into the stone age in one fell swoop. These mobile suits were designed for the explicit purpose of interstellar warfare, each expected to take on the military forces of an entire planet and win. All this from an ostensibly Real Robot series.
The Porsche 917 was such a good race car that the Le Mans organizers rewrote the rules after the 1970 season to ban it.
Pog has 2. One, Unoffical slammers were often larger and thicker than official Slammers, making it much easier to score if you were using then, for no real drawback. A much better one was to simply throw the slammer at the SIDE of the pile, which could often knock over more than half of the Pogs on turn 1, rendering the game unwinnable for anyone else.
From the book series Animorphs there's Cassie, who right from the start is an estreen, a character naturally skilled at morphing. She is one of two characters seen with this ability, the other being a One-Shot Character and thinly-veiled Deconstruction of Mary Sue-type characters. Later they go even farther, with Back to Before revealing that Cassie is a 'temporal anomaly', an exceedingly rare creature with a spatial sense so superhuman her very presence undoes the timeline-meddling of a Reality Warper.
In Edward D. Hoch's short story Centaur Fielder for the Yankees, the New York Yankees sign on a centaur. Think about that.
A parachute can turn an egg-drop competition into a joke: if it can handle a ten-foot drop, a parachute-equipped egg can survive being dropped from any altitude up to the point where you need to worry about surviving orbital re-entry. Consequently, many egg-drop competitions ban the use of parachutes.
Fate/stay night's Gilgamesh is considered to be so ridiculously powerful that he could easily take on every other Servant in the war AT THE SAME TIME.
Gilgamesh is so broken that Tokiomi declares victory the moment he confirms that he's summoned him.
The Order of the Stick (set in an RPG Mechanics Verse based on 3rd Edition D&D) parodies this when Roy meets a half-ogre with a "perfect" character build. Due to his size, his wielding a spiked chain (a reach weapon), and his combat reflexes, he was able to score multiple attacks on Roy every time he approached by jumping backwards. After boasting about how invincible he was, he ended up jumping back a little too far and going off a cliff.
During both World Wars the British Royal, British Commonwealth, and American Navies had access to the then current editions of Jane's Fighting Ships. This might not seem like much of a game breaker until you realize that those books contain very detailed technical information about almost every major surface warship that was afloat during both of those wars. Many of the silhouette line drawings in those tell you how thick the deck armour was and how the side armour was distributed.
Humans would qualify, especially after The Industrial Revolution or the advent of agriculture. Fire alone is enough to qualify the whole species as a MASSIVE, MASSIVE gamebreaker.
Several moves in Kung Fu Panda could qualify, but Tai Lung's nerve attack stands out. It paralyzes his opponents by blocking their chi, rendering them helpless at his own hands.
Squirrel Girl has the power to talk to squirrels. She also has the power to manipulate them to attack her opponents. It might not seem like much, until you see them ganging up on◊ Doctor Doom of all people, then you realize that they are vicious.
Heck, those squirrels alone are what make her one of Marvel's most lethal heroes.
As if the SaintofKillers wasn't bad enough, he wields a pair of walker colt revolvers forged with the steel of the sword of the Angel of Death. They fire bullets that are completely impossible to avoid or survive. Even worse is that they neverrun out of ammunition & never misfire.
In Fairy Tail, during the Magic Tournament arc, one game has a house with 100 monsters inside, whose strengths vary from scary (D class) to not even mentioned (S class). Each competitor picks the number that they want to fight at one time, but only gets 1 point per monster (regardless of class), and can't leave until either they or the monsters are dead. So Erza picks all of them. Even though she only needs 51. When she's done, the other 7 competitors are reduced to punching a device to measure their power level.