In Sonic the Hedgehog 2, all seven Chaos Emeralds could be gathered in the first zone, since there are enough checkpoints in Emerald Hill Zone to get all the emeralds. This (naturally) allowed you to breeze through the game casually, the only challenge being the final level, in which the player has to fight Silver Sonic and Dr. Robotnik with no protection.
Sonic 3 And Knuckles
Really, in the retro Sonic the Hedgehog games, Super Sonic is a Game Breaker. Faster than normal Sonic, can jump higher, and is invincible to everything bar death pits, crushing and drowning. The only drawback is that once your rings run out you're defenseless unless you managed to pick up a shield, but rings are easy enough to come by, especially in Sonic 3 & Knuckles. Speaking of which, Hyper Sonic, Super Tails and Hyper Knuckles are even more Game Breaking because of their abilities. Hyper Sonic can destroy all enemies on screen by double-jumping, Hyper Knuckles can do it by gliding into walls, and Super Tails's Flickies will automatically home in on and destroy any enemy near them. Bosses with Super Tails become a joke because all you have to do is just stand there and let the Flickies do all the work for you. Super Sonic is such a Game Breaker that it's easy to see why Sega made it an Eleventh Hour Superpower in their newer games. Another Game Breaker in a meta sense is the acquisition of emeralds in 3 & Knuckles; the giant rings come back if you leave the game and reload, so you can keep using the same one in Mushroom Hill, which means the only hard part is actually completing the Special Stages.
Super/Hyper Sonic becomes an even worse Game Breaker in Sonic 3 & Knuckles once you pick up the electric shield, which magnetically pulls rings towards you, and as long as you can move through the level consistently quickly, you can pretty much stay Super/Hyper through the whole level.
Also, even without Super/Hyper Sonic in Sonic 3 & Knuckles, each of the shields in the game trivialized bosses and several levels. whether it was the fire shield to allow players to stand underneath most bosses and jump. or the electric double that ruin the whole point of the boss being out of reach. Heck, even Sonic's Insta-Shield's reach is just enough to break several boss battles if you time it correctly. A definite fan favorite is the fire shield for the otherwise intimidating Lava Reef boss, which allowed Sonic to walk on lava and laugh off every attack except the spike balls at the end of it.
There is one instance of Super Tails backfiring. His swarm of Super Flickies automatically targets enemy units. But the Death Egg Act II boss can only be hurt by using the gravity-switching elevators to knock its drone units into it. This is next to impossible when they keep getting destroyed by Super Flickies. So he's broken in a good way and a bad one.
In addition, Super Tails can render the Sandopolis miniboss, the Stone Guardian, unwinnable, but only if you stand to the left of the boss to make it face left. If facing left, the boss gets knocked to the right and away from the quicksand pit , which can happen pretty easily with the Flickies. However, if you stay to the right of the boss and make it face that way, the Flickies will knock the boss towards the sand pit.
The Super and Hyper mode were 100% completion type bonuses which took a while to unlock and gave you the true ending, so it was seen as an award for doing so (the first Sonic had emeralds but no Super/Hyper mode and they added in there to reward the player. It might have been removed because using it at insane speeds on casual stages would have been more difficult.) so it doesn't intrinsically ruin a normal runthrough of a game, and it *is* optional. Also, to get super emeralds, you have to first give away your chaos emeralds, which means no Super Sonic while gathering emeralds for Hyper Sonic. The lightning shield did make some fights easier (like the fire shield did on fire bosses since you were immune to all of their attacks), but the game wasn't a cakewalk with it. So YMMV.
Not even a "super" character, Tails in Sonic Adventure becomes something like this in some of his levels due to his flying ability. In Windy Valley, you can skip the entire level just by flying over everything. Other levels, such as Sky Deck, become laughably easy once you find all of the short cuts that you can reach just by flying.
Sonic Adventure 2
Sonic is this if you have acquired the Magic Hand and the Bounce Bracelet upgrades. For the Magic Hand, you can have the option to turn your enemies (except ghosts) into balls and for the Bounce Bracelet, this can be useful for the two Shadow boss fights and the Big Foot boss fight. For the former, just quickly defeat Shadow by repeatedly using the Bound Attack and for the latter, you can use the Bound Attack to get a good height to home attack Big Foot without having to stand on the boxes.
Sonic Advance 2
Cream in Sonic Advance 2 renders every boss powerless as her Cheese attack move will always hit from any distance during the fight. Simply pressing B repeatedly without even moving can guarantee an easy victory.
Cheese does that in every single Sonic Advance game, trivializing all but the Super Sonic bosses.
In Sonic Advance 3, all you have to do is choose Knuckles as your main character and Tails as your partner. This combination increases both Knuckles' gliding ability and Tails' flying ability to an insane degree and allows you to beat most levels easily.
Tails is cheap thanks to the fact that his Spinning Tails attack does damage to the boss from below, considering most bosses are designed to be hit from above.
Amy Rose may be more of an example of Difficult but Awesome, but using her hammer attack on springs in Sonic Advance and Sonic Advance 3 makes the spring launch her twice as far, often times sending her soaring over large chunks of the level. In Sonic Advance 3, having her as your partner replaces everyone's ground attack with a hammer attack similar to hers. Enjoy your flight.
In Sonic Heroes, there was Team Rose who was supposed to be the game's version of easy mode, but they took it to the next level considering that their Team Blast gauge charged up extremely quickly, and once it was at full power, their Team Blast destroyed all the enemies in the vicinity, gave them a shield, Power Sneakers, invincibility, and powered them up even further by instantly raising each character an entire level, which made reaching the max level of 3 all too easy. Combine this with the fact that their levels are about half the length of the other teams levels, and you have absolutely no reason whatsoever to struggle to beat their portion of the game.
From Sonic the Hedgehog (2006) we have Sonic's Purple Gem custom action, which turns Sonic small by holding down a button. It may seem like a novelty at first with the high price of 14,000 Rings, but you'll realize why it's a Game Breaker. While small, Sonic's Homing Attack is replaced with an infinite double jump. This allows you to pass some sections of Action Stages just by double-jumping or easily find Silver Medals. And you can buy this ability right before Sonic's final level.
Oh, and on a lesser note, Sonic's Red Gem custom action, which slows down time. Including the in-game timer, making it a bit easier to S-rank some missions.
Also, it's possible to skip large sections of Omega's levels thanks to a bug with his hover function. Essentially, pressing the hover button in midair makes Omega cancel all vertical momentum briefly. This means that, by rhythmically tapping the hover button, you can make Omega fly. This also allows Omega to visit places he isn't even supposed to go, including Shadow's section of Wave Ocean (you even get Shadow's dialogue!) and Sonic's, though the latter has no enemies to fight.
Cream the Rabbit from Sonic Chronicles. Seeing as you barely have to go out of your way to get her on your team, she definitely applies here. She has a move called "Refresh" that, when used, restores PP for everyone on the team. She can also heal everyone at once, rid everyone of status effects at once, etc. Her inputs kind of tricky? No problem. Equip her with Ferox, a Chao that makes all POW moves never fail, and watch the game suddenly become piss-easy.
Also, that move Refresh? It also affects Cream, and at rank two (which you can get the minute you recruit her thanks to Leaked Experience) the move costs 8PP and restores 10. That's right, It pays for itself, meaning everyone else can perpetually use POW moves for absolutely no cost.
Super Sonic returns to his Game Breaker status in Sonic Colors. Though sort of an Infinity+1 Sword due to how long it takes to get him (you have to first obtain all Red Star Rings, which there are five of in every stage, then you have to complete all the Game Land stages, which are seven stages with three acts each), getting him will tear the game apart. The main reasons being that for one, he can boost infinitely, for two, you get a 2000-point "Super Sonic Bonus" every second you spend in Super form, and for three, just using him in a stage means you're guaranteed an S-rank, no questions asked if that stage has no Wisp other wise your not getting an S-rank anytime soon.
The DS version gives us Unlimited Boost which not only lets you still use Wisps can be used on all modes and acts even bosses that isn't the true final boss, Sonic Simulator, or time attack.
Super Sonic has similar attributes in Sonic Generations, too (both Classic and Modern). They attempted to nerf him by making his rings decrease much faster when boosting and in 3D sections, boosting made you fly. While this made you bypass all obstacles in 3D sections, you wouldn't be replenishing rings either. That said, you can still just not boost and enjoy invincibility.
The Act 1 shield powerups. The Flame Shield lets you air-boost to speed through linear and open-air sections, and the Thunder Shield allows you to double jump.