In no particular order: Final Fantasy IV-VI, Super Mario World, Super Mario RPG, Super Metroid, Super Punch-Out!!, NBA Jam, Donkey Kong Country, The Legend of Zelda: A Link to the Past, Secret of Mana, Secret of Evermore, Terranigma, Ninja Gaiden Trilogy, Breath of Fire I & II, F-Zero, Super Castlevania IV, Chrono Trigger, Super Mario All-Stars, Kirby Super Star, Contra III, Mega Man X, Street Fighter II: Turbo, Gradius III, Earthworm Jim, Arkanoid
I'm probably forgetting some good stuff
edit: Oh yeah, Earthbound. Dunno how well it has aged, though.
Also, if you haven't ever played Starfox you might as well check it out, but it's pretty much unplayable these days