Thanks to Alessandro for alerting us to kunstderfuge, the largest resource of classical music in MIDI format online. kunstderfuge is a subsidiary of OnClassical, the CC-friendly Italian net-label we featured earlier here.
At kunstderfuge, there are complete piano works by Beethoven, Chopin, Haydn, Mozart, Bach, original piano rolls (including sacred hymns, medieval and renaissance music, and ragtimes), and much more, all available in MIDI format. The files have been produced by a variety of contributors and are ordered by composer, making them easily searchable.
Since 2004, many of these MIDI recordings have been released under a CC license. Just recently, kunstderfuge chose to release a plethora of new MIDI sequences under a CC BY-NC-SA license, meaning there are now a total of 2,192 MIDI files (13.3% of the entire collection) published under a license that allows you to use the files for any purpose outside of commercial intent. Very cool!