Warning: not a game synopsis, but very cheap cheats. Read at your own grubby risk!
In "Sonic the Hedgehog 2" (the best Sonic game, IMO), there are two ways to achieve the feat of playing as "Super Sonic" or "Gold Sonic," where once you gain 50 rings you can jump very high, run really fast, and be pretty much invincible and super-hedgehogish. (Understand, though, you can't do this on the Master System, thanks to Xenex for the correction.)
1) Collect all of the Chaos Emeralds in the "Special Stages" that you get into after passing a star post thingie (checkpoint) and jumping through the psychedelic loop of stars that subsides. There are 7, and depending on how much time you dedicate to the craft, it can be either hard-as-hell and nerve-racking or boring (There are 7 posts in the 2 Emerald Forest levels; if you're awesome enough it's a cinch.).
2) Go to the "Options" screen and in the "Sound Test" enter the numbers 19, 65, 9, 17. Press start. The game will restart to the title screen. Select "1 Player" by holding "A" and pressing start. Now, you're at the "Level Select" screen, where you can warp to any level in the game. Go to the sound test on that screen and enter the numbers 4, 1, 2, 6. A "superhero" sound should result. Now you can play as "Super Sonic".
You can also pause the game and press "A" to restart it, "B" to play in slow motion, and "C" to make the game go by frame-by-frame. Supposedly, this is called "debug" mode, for which there was a separate code but it works with the Super Sonic code. To go back to the "Level Select" screen, just hold A and press start as before.
While Sonic can enjoy such things as jumping 3 times as high and running fast enough to go through walls if a hill is steep enough (glitch), Tails can't become "Super Tails" due to a cut in the massive original plot. Oh, well.
As an aside, it is supposed to be impossible to become "Super Sonic" in "2 Player" mode. I've done it once, but I don't have the faintest idea how. It was fucked up and really, really, cool, and I couldn't turn off the game (like the free porn episode of "Friends").
Super Knuckles, (also called "Silver Knuckles," but should have been of the "brass" variety) by the way, kicks much more ass. You can only obtain the ass kickness the hard way, through the Chaos Emerald route (after plugging in your "Sonic and Knuckles" cartridge, of course...which has no menu to enter cheat codes...blasphemy!).