Donkey Kong Country 2 has permanently effected me as a gamer. It's the perfect mix of challenge, sound, visuals, and gameplay. The already massive overworld is extended through the Lost World, and leads to a really epic, unforgettable scene. DKC 2 will forever be my favorite game.
I can't forget about the other stuff, though, much of which I still continue to play. The SNES is home to my favorite Mario (or Yoshi, I guess), Zelda, and Kirby games.You're really not a gamer until you've beaten each of them. There's also the uber-challenging Super Ghouls N' Ghosts, the puzzler Tetris Attack, and the 3 Mega Man X games.