Once more, I cannot just post one game. I love multiple SNES games too much to just pick one. So instead I'll post a list of my favorites.
Super Mario RPG: Legend of the Seven Stars - One of the best RPG games of the SNES. Square Soft did an amazing job and taking Mario and making it into a RPG. I played this game countless times and loved it every time. Great game play, great characters (Geno!), awesome music, and an amazing secret boss.
Final Fantasy Mystic Quest - My first Final Fantasy game and one of my favorite games to play as a child. I thought it was extremely fun and interesting, and still do. I see a lot of hate on this game, but I don't think it deserves it. I enjoyed the game play and having multiple weapons. Had some memorable music as well.
The Legend of Zelda: A Link to the Past - What is there to say? One of the best LoZ games (the best in my opinion). Great game play, awesome dungeons, plenty to do and a great story.
Yoshi's Island - An amazing game that focused on my favorite Mario character. Such a fun game with a really cute theme and awesome music.
Donkey Kong Country/Donkey Kong Country 2 - Amazing game play, awesome music, and had the feature of co-op.
Final Fantasy VI (III) - I never owned it, but I borrowed it for a while from a family friend. Really enjoyed it from what I got to play. It wasn't until the PS1 port that I got to play it again.
Super Mario World - Lots of fun worlds and ability for two-player. Led to hours of fun.
Super Mario All-Stars - It had Super Mario Bros. 3, what other reason would I need? =P