Most of the songs listed are basic (well, I play them in basic form unless I save other parts of the song to my keyboard or know some chords for the song) since I haven't had any formal training:
Donkey Kong- All songs and SFX
SMB- All songs, and I know the power-up sound, power-down/pipe sound, hitting a ? block sound, coin, time-running-out thing, etc.
SMB2- Just a couple songs
SMB3- All songs, basically, save for just a few. Also, I figured out the stage-flipping-over sound after you complete the level and return to the map screen (for the SMAS version), and the sound of the timer being counted for points.
SML- Overworld, underworld.
SMW- All songs, save for just a couple. Also figured out the death theme, and the SFX when you release a reserved item.
SMK- Koopa Beach, Raceways, few more. Also figured out the notes for the "item roulette." (I like DS' the most since it changes depending on course)
MK64- Luigi Raceway, few others.
MK:DD- Luigi Raceway, couple others.
MKWii- Trying to learn some of the songs, really haven't worried about it. Wanna learn Maple Treeway.
Mario Golf- Toad Highlands, Shy Guy Desert.
MG:TT- Peach's Castle. (I have two other parts saved to my keyboard). Also, menu screen (love that song).
Mario Tennis/MPT: Some songs.
Sunshine: Delfino Plaza, some others.
Galaxy: Observatory, Good Egg, Battlerock, Space Junk, the weird song that plays in the cube thing (where you chase the notes the very first time at Good Egg), and just recently learned Beach Bowl, and Rainbow Mario. (The only thing I need help with on that song is the harp played in the background that is played very fast. No one ever offers any advice or knows what I'm talking about, so please... anything?)
The Sims: One of the "buy crap" songs.
Legend of Zelda Ocarina of Time: A few (I don't boast that I can play the main theme because that is like the ultimate cliche now). Also, learned the little bit that's played with an ocarina when morning comes.
Wind Waker: Great Sea, Cursed Great Sea, the forest place, Outset Island, a few others.
Rally X: Intro song, main song, bonus song (I combine the main and bonus for a medley of sorts so the bonus portion of the song really sounds like a solo of the main song) Also, found out the sound effect for when you get a Special Flag and it's counting your fuel.
Many, many more. Oh yeah, I learned all the city songs (save for California) on the SNES version of Mario is Missing (aka, the best arrangements of Super Mario World, ever). Also a few from Mario's Time Machine.
If you read that above, you'll see that I have a knack for trying to figure out sound effects from games like power up, power down, reserved item release, etc. Playing those sound effects in conjunction with song just kinda helps it come to life a bit more and reminds people of the most recognizable sound effects in Mario games (for non-Mario-ish people).
My power up sound is made with "Gameboy" sounds on my keyboard (sounds exactly like it, voice #387 on my DGX-200) and speeding it up makes it sound like the Power-Up SFX used for the mini-game Mushroom Titan in MP3.