MIDI is still cool after all this time
OGG - 2003
Ogg is a container format and it is mostly used with the vorbis audio codec. For development use libogg and libvorbis.
MP3 - 1993
License crap, ignore mp3 and use use OGG.
WAV - 1991
Waveform Audio File Format that is a common format on windows.
Module (.mod, .s3m, .xm) - 1987
Group of formats used for music with the same basic setup. A bit like a MIDI file but a module also contain the sounds samples that the notes play.
MIDI - 1982
Interface created to allow electronic musical instruments communicate with one another. Midi files are like note sheets that tells a instrument when to play a note and what parameters to use. There are up to sixteen channels of information and it's possible to switch the instrument each channel is using. The midi file does not contain the sounds as they are part of the device playing the the midi notes.