Music Sources
vgmrips.net has video game music rips in VGM format. They may be converted to midi format with vgm2mid.
bitmidi is a midi sharing website mostly useful for finding popular contemporary music, video games tracks, and show tunes.
Online Sequencer has tons of user-submitted midis with plenty of remixes/adaptations of other user-submitted songs.
Tools
Online Sequencer is a useful website for creating, sharing, and remixing music in midi format. It is likely one of the most active midi sharing websites.
musictomidi.com can convert mp3, ogg, and wav files into midis. It features an interactive sequencer as part of the output, which can be combined with Online Sequencer to assist with manual conversion.
MIDI Transform is a paid program for Windows that may be used to re-scale a midi file's volume. It is available as a demo without file-saving ability and was created with .NET.