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.
This still happens with a shot clock but is thankfully limited to the end of the game. When the game is close enough towards the end that the trailing team thinks they can come back to win they will foul the leading team whenever the leading team has the ball. The team that is leading when intentional fouling starts almost always wins. This strategy tends to annoy the fans of both teams.
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.
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 spartan from Deadliest Warrior the Deadliest Warrior video game is a bit of game breaker. 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.
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.
An early version of Monopoly for cellphones (in the pre-smartphone days) had incredibly stupid computer AI. When the computer offered a trade, you could modify the offer, asking the computer to add all its undeveloped properties to the trade (except for properties in the same colour group it wants to trade from you), and it would accept the trade no matter how bad a deal it was.
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 two. 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 one, rendering the game unwinnable for anyone else.
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.
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.
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.
The White Water pinball machine has a mode that makes everything worth 5 times as many points for the following 25 seconds or until the ball drains, whichever comes first. Whenever White Water shows up at a competition, it soon becomes a race to set up different features to yield as many points as possible, then activate that multiplier. It is not uncommon to see people doubling their score or more within those 25 seconds, and any competitor who fails to reach that multiplier is certain to lose.
During both World Wars the British Royal, British Commonwealth, and American Navies had access to the then current uncensored 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. All of the following was contained in one easy to reference source:
Silhouette line drawings and/or photographs of almost every class of ocean going surface warship (including obsolete and minor ones) in the world.
Many of the silhouette line drawings tell you how thick the side armour was and how it was distributed.
The planview line drawings almost always showed the weapon layout and often included information about firing arcs.
Many entries include information about deck armour and underwater protection. Some have a thick line in the silhouette drawings indicating where, in elevation, the deck armour is located and/or vertical dashed lines showing the location of the watertight transverse bulkheads.
Information about things like fuel bunkerage, fuel consumption, fuel type (coal, oil, diesel, or mixed), engine horsepower, maximum speed, and cruising range is extensive.
The WWI editions had some fairly detailed information about individual models of naval artillery (shell weight, powder charge, muzzle velocity, range, and more), charts of major harbors with depth and tide information, and information about the size and number of the dry dock, floating dock, and refueling facilities available at those harbors.