Awesome mech game with great graphics and a great sense of "weight". The final cutscene was removed from non-Japanese releases of the game.
Donkey Kong Country
Great graphics, controls, soundtrack, and level design, along with a host of minigames. A bit unimaginative, but superbly excecuted and very fun.
Earthworm Jim 2
The first one was better on the Genesis (the SNES's low resolution reduced the field of view, making its version of the game less fun), but this one is best on the SNES. I'd say that there are more minigames than there are proper levels!
Front Mission: Gun Hazard
Produced by Square, a company better-known for its RPGs. It's a mech game in the vein of Cybernator, but it's even better than that one. There's a lot more strategy, and the graphics are mind-blowing.
The Lost Vikings
There are a billion versions of this game, but the SNES has the original. It revolves around teamwork-based puzzles, and it's designed beautifully.
Yet another mech game! It's very, very similar to Cybernator, but with the awesome addition of the ability to exit your mech and steal a different one. There's also a lot more action, and the level designs are great. There's even a deathmatch mode!
Super Mario World
Actually, I don't really like this game very much.
Ah, that's better! This game is the pinnacle of the Metroid series, and consequently of games that involve exploring caves while shooting stuff. Everybody needs to play this game at least once.
A game about a girl who climbs around by using her fishing pole as a grappling hook. It's pretty fun, in its own physics-y way.