A few MIDI's that I've exported using unfinished Spc2Midi. They are not particularly good, since they are raw exports. However, with the right tools, someone else could improve the instrumentation. For another good utility that can export MIDI's, try SPC Tool, or for some real songs, go to the Videogame Music Archive or Overclocked Remixes.

Exported SNES MIDI's

Mario World intro Koji Kondo The first song to work correctly and turn all my effort into an unbreakable smile (at least until the next day :).
Mario World - mistuned introduction Koji Kondo (sort of) When I was still perfecting the pitch to note conversion, the translation was skewed and Mario World came out sounding like this, but it actually sounded kind of neat to hear such a familiar song in a minor key.
Seiken Densetsu 3 - Strange Medicine Hiroki Kikuta ...
Seiken Densetsu 3 - Where Angels Fear to Tread Hiroki Kikuta Instruments were added by Gideon Zhi
Donkey Kong Country - Introduction (unknown) ...
Mario RPG intro (happy adventure) Koji Kondo, Nobuo Uematsu, Yoko Shimomura Peppy song, not necessarily my conversion of it to MIDI, just the song itself.
Chrono Trigger - Enemy Battle (unknown) If you know the game, you'll know the tune.
Mario World 2: Yoshi's Island (intro) (unknown) Not the best sounding as far instruments, but it has all the notes.
Zelda: A Link to the Past - Main Theme Koji Kondo The theme music that makes a Zelda game a Zelda game.

Some of my Favorites (not SNES exported)

Zelda TOC Gerudo Valley John Kuzma From Zelda 64.
Chronotrigger Ending Theme By Yasunori Mitsuda
Sequenced by Pokey
From, in my opinion, the greatest SNES RPG.
Sailor Moon Cantonese Theme Altered by Ashley, Vivian, Karen, Linda From Sailor Moon
Saria's Song By Jeff Chermak From Zelda 64
Saria's Song Remix By Freddy Meijer (icq: 13778829) From Zelda 64. You'll like it - just listen.
Tutatta Tutatta? Totally unrelated to video games, but so loved, since it was the first taste of electronic dance music for me, back when the Internet was relatively young and MP3's were unheard of. The clue to its origin is a single string (name of author or song?).

Some of my own practice recordings

Unchained Melody Recording: Dwayne Robinson, Original: Righteous Brothers An old recording of me playing the Righteous Brother's tune from Ghost. I would never upload this to anywhere more prominent.
One Man's Dream Recording: Dwayne Robinson, Original:
Another old recording of me playing Yanni's "One Man's Dream". *There are mistakes in this, so I would never upload this to anywhere more prominent.