In many sports games, especially American football games, there are money plays that work 99% of the time against the computer. For example, in the Madden series, curl routes against a CPU defender in man-to-man coverage is an easy completion.
Likewise, any kind of play action rollout which targets a tight end running a post corner route. Man-to-man coverage is almost useless, and if you keep the QB moving the same direction as the TE, any defender in zone coverage will peel off and head for the QB, leaving the TE undefended for a quick pass. Unless the defense brings the house in on a blitz, this play is almost always a guaranteed completion, for at least ten yards at minimum, and if the TE breaks free of his coverage, he can cover 20-30 yards along the sideline easily.
Passes to the fullback in the flat work similarly.
When run correctly, power sweeps to the wide side of the field are literally impossible to stop.
In Smackdown Vs. Raw 2008, the Hardcore wrestler type can heal themselves by smacking themselves in the head with a steel chair. This becomes a Game Breaker in Money in the Bank Matches and Table Maches, as the former requires endurance, but Hardcore can heal that off, and in Table Matches, red damage is required before you can be put through a table. In other matches, this also makes a comeback very easy.
Various characters in WWE Smackdown vs. Raw 2009, due to the Signature / Finisher game mechanic and the fact that being hit with them in a row is a guaranteed loss. Most characters cannot take advantage of this, but certain ones (for instance Undertaker, Kofi Kingston, and especially Triple H) can and therefore if they build enough momentum become unbeatable.
WWE Smackdown vs Raw 2008 was even worse, having special abilities being available based on what sort of wrestler you were (ie, brawler, dirty, powerhouse, high flyer), EVERYTHING becomes completely pointless next to the Powerhouse's ability, which makes all their grapples uncounterable, and makes them instantly counter all attempted grapples on them. They even shrug-off attacks. This completely destroyed any and all semblence of a fun gaming experience in multiplayer matches.
To wrap all this up some classes are Gamebreakers in particular match types.
Hardcore: Table and Money In The Bank(See Above)
Powerhouse: Last Man Standing (can get up instantly)
Brawler: First Blood (you can sit on them and continuously pummel their face, a very damaging bleed move)
High Flyer: At end match where pinfall is an option. (Possum Pin is too strong, and you will likely both be very damaged.) and, when Stamina is turned off their rolling dodge makes them invincible.
Yet again from the Smackdown vs Raw series is the ring rope environmental grapple from 2007. It was highly damaging, drained momentum like crazy, and was unblockable. Later games at least curbed the pain by making it counterable, but then we got...
The ground and pound, as noted above the ability to sit on your opponent a dish out knuckle sandwiches until you got tired or they countered one of them, but considering each punch had a very small counter window, the poor punching bag often had a very damaged and often bleeding head and no momentum. Later years made it worse by the fact that now every one can do it and the computer practically abused both it and you.
And there is a new ring rope grapple, by dragging your opponent face down into the ropes, you will put their neck on the bottom rope, and push with the foot. Normally, as in Real Life wrestling, the ref gives you a 5-count, and it you don't let go, you get DQ'd. Not bad. No DQ, or the referee's knocked out? you can go at this for about 10-12 seconds, which does insane damage, and almost guarantees full momentum, the onlydownside being if you hold it until you let go automatically, you get counterattacked, due to being exhausted. Not that you could let go about a frame before and not get tired or anything.
Once more from Smackdown, good luck finding anyone online with a high rank not over using the Head Attack (ungodly range and overly long stun), Buzzsaw Quick Kick (overly long damaged animation, during which you can be attacked again), and the Striking Spear (the longest ranged running strike attack in the game).
Also, look at the abilities they have. If it says 'Fired Up' and 'Fan Favourite', now you know why they win. To explain, Fired Up will, once a match, and ONLY if you have a finisher ready, give you 3 finishers to do. Fan Favourite will, once a match let you do a special taunt that gives full momentum (i.e. a finisher). Finishers have a pathetically small counter window, also, so This Troper, who is normally a well-timed countering god, has only protected myself from a finisher ONCE.
Don't forget Christian Okoye (same game, same website). If his condition was good enough, most defenders literally couldn't even touch him.
Tecmo Super Bowl had a LOT of these, actually. Jerry Rice would catch nearly 100% of all balls thrown his way. QB Eagles (Randall Cunningham) was one of the fastest players in the game and also had superior passing abilities. Worst of all, though, was Lawrence Taylor, who was such a dominant pass rusher he could get to the QB at the same time as the ball, leading to an instant sack 99% of the time.
Many EA Sports BIG games starting with NBA Street have literal Game Breakers. These are pretty much just power-ups. In NBA Street, nailing a shot with one of these would give you points while taking away from the opponent's score, whereas in NFL Street, they pretty much worked like an Invincibility Power-Up. The sequels to each gave you the Game Breaker 2, which was pretty much The Same but More.
Madden 08, on the PC at least, has a couple of huge game breakers in its franchise mode. The first has to do with the draft: early in the season, before the trading deadline, the player can trade their first-round draft pick for any other team's first-round pick. It doesn't matter if the player picks last in the round, and they're trading with a winless team who may wind up with the first-overall pick, they always make the trade, and will throw in two extra picks. Depending on the team, you may get their picks in rounds 1-3, or in rounds 1,2, and 4. So with that #32 pick in the first round, you can get a pick in the top 10, plus two other high-round picks. This works every season, so there's no draft-position penalty associated with on-field success. Especially since at draft time, teams will offer a first- or second-round pick for every pair of picks in rounds 1-6. It's not uncommon to draft five players in the first two rounds and one in the seventh, year after year, guaranteeing that every draft loads the team with eventual Pro-Bowlers. The second game breaker is triggered after several successful seasons, either a certain number of Super Bowl victories or undefeated seasons. All veterans' "awareness" rankings will shoot up to 99 during the offseason. Once this happens to a franchise, it's rare that they will ever lose a game again.
Thankfully, the modders managed to fix most of this stuff on the PC. The in-season trading, however, was not fixed and will never be.
Madden 04. Say it with me now: Michael Vick. This guy could give Bo Jackson a run for his money. For those who don't know, Michael Vick was, at the time, QB for the Atlanta Falcons, and had emerged as one of the first successful dual-threat QBs in NFL history. Madden games have a tendency to make the cover player into Game Breakers (take a look at Troy Polamalu and Larry Fitzgerald in Madden 10, and Vince Young in 08), but they took Vick Up to Eleven. He had a max speed rating, something rarely attained by even RBs and WRs. He also had elite ratings for stuff like throwing accuracy, despite throwing for less than 55% in the season prior to becoming the cover boy (for reference, 65% is generally considered a top tier completion percentage). Basically, if you paired him with a great WR, you could score on pretty much every play. Call a Hail Mary on every play. If your receiver is too well covered, scramble and dodge defenders, all of whom are deep downfield, for a relatively easy TD. If he's even slightly open, throw to him and you'll almost never miss.
Triple Play 98. The Oakland Athletics had a pitcher, Richie Lewis, who (aside from being a short pitcher at 5'6) was rather unremarkable. He threw a mediocre fastball (88-90 range)... and a few other pitches (such as the slider) at between 111-120 mph. To put this into perspective, one should realize the fastest fastball (with almost no movement) was only 105 mph.
The entire offseason in MVP Baseball 2005 was completely broken, in that if a player was considered a free agent come offseason time, it was trivially possible to 100% guarantee they would sign with your team, leaving you with a full team of the best free agents on the market. Not helping matters any was a Good Bad Bug that allowed you to completely disregard another team's higher offer and sign the players you wanted for their minimum asking price, which was already lower than normal for players of their caliber. Even if the free agent market happens to be dry, simple Save Scumming can fix that.
In Pro Evolution Soccer 2012, the skill card "Speed Merchant" increases the player's speed and allows him to take sharper turns. So, you can either learn every little aspect of the game, from tactics to defending, keeping posession, outplaying the opponent in every part of the pitch... OR you can pass the ball to Messi, run past the opposite defense and score. Konami already nerfed it a bit on their 1.03 update, but it's still a Game Breaker.
Playing FIFA online, equipping two pacey strikers (or indeed a pacey winger with a striker) means that most players can skip past defences, force the goalkeeper to run out, and pass it through to the other striker for an effortless goal - since the goalkeeper will, by this point, be on the opposite side of the box. Such a tactic is often done in spite or by those not good enough to score better goals. Or indeed those willing to look like a dickhead to win.