I just found a great resource for piano MIDI's. Seems to have thousands and all of them are free to download.
I really must place some emphasis on this site, http://www.hamienet.com
is fantastic for popular music!
My list of most used and relied upon MIDI resources:
First stop for all anime related stuff! It's mostly sheet music, but quite often there is a MIDI or a MUS to go with it. If not, and you have enough time, you could copy by hand the notes into a program like Finale (the paid one) or MuseScore http://musescore.org/
(free!) and save the midi file. (Remember to separate left and right hands on to two different tracks!)
This is a pretty neat little resource too. Has quite a few little fringe animes.
Nice collection here too.
This is actually a Youtube channel dedicated to synthesia demos of MIDIs made of KyleLandry's performances and improvisations (http://www.youtube.com/user/kylelandry
). The midi files are linked in the descriptions of the videos.
Vocaloid: (not quite anime, and big enough for it's own category)
General MIDI deposit, many are simplified.
This one's a bit more complicated, but if it's there, it's usually much better quality. On the right is a menu with the beginning consonant/vowel, (YOU WILL NEED TO KNOW THE JAPANESE NAME OF THE SONG TOO!) so look over there, and you will see a list of links underneath (NikoVideo.jp is just a japanese youtube). If you're lucky, (like I was with ダブルラリアット "Double Lariat") you might find a link in the video's description (you have to register to view the video, but not the description) usually accompanied with a password immediately before or after it. Good luck with this one, it's rare, but exceptional quality.
Most games with memorable music will have a few midi's here, there's also a small anime section. (The Sims piano songs in Build and Buy modes are always a favourite!)
Extraordinarily comprehensive Final Fantasy MIDI and sheet music one stop shop.
Final fantasy Piano Collections midis from Square (Enix) themselves!! VIII, IX and X have midis (not VII however...).
I'm not even going to begin to list, it's public domain so it's everywhere. It's better if you know what you want to play... look at what people play on youtube and then google the name, composer and "MIDI"... you'll find what you want.
MUS are proprietary files similar to midi (nicer sheet music formatting though, so it's often used). You can get a free little MUS to MIDI converter here: http://www.fit.vutbr.cz/~arnost/muslib/index.html
called "Quick MUS -> MIDI file converter v2.0"
If you're learning or practicing how to read sheet music, I strongly recomend you get software like MuseScore (linked above) and make random midi files using crotchets ♩ ("quarter notes" for you americans) along the part of the scale you need to know (up to 2 ledger lines above and below both treble and bass clef at least
). Remember to make it progressively harder, start off with progressive ups and downs, then same with certain spaces, then gradually get more random. also at some point throw in sharps and flats and just keep practicing and practicing (make the sheet music the biggest it can go, no looking at the piano roll!) and you should eventually get the knack of it
(I think I might add that in as a feature request, random generation of notes for reading practice with difficulty levels.)
So yeah, hope this helped!