As far as platformers go, Aladdin has always been a personal favorite, along with Super Mario All-Stars, Yoshi's Island, Super Mario World.
If you like RPGs, I'd say The Legend Of Zelda: A Link To The Past, Chrono Trigger, Secret Of Mana, Seiken Densetsu 3, and FF6 are the best games available, and Harvest Moon is also a pretty popular RPG/sim/strategy game.
The F-Zero games are fun racing games along about the same lines as Mario Kart (which is also great).
I enjoy playing Goof Troop from time to time. It's kind of a more puzzle-oriented version of A Link To The Past.