.wav is uncompressed music... It was included with windows from 3.x series (if not allready in dos, that I can't remember)...
They take up much space, which is why we have other formats....
WMA is M$'s own standard, which gives a better compression than .wav without loosing too much quality..
.mp3 is another way of compressing music, developed by Frauenhofer afaik... they started charging for it, and mp3pro, which gave rise to
Ogg Vobis... A free format, though not widely adopted yet...
You also have .mid/.midi which is synthesized music... It was used widely in games in the early/mid 90'ties...
Then there are .xm and .it, which are other ways of creating synthesized music, much used by programs like fasttrack and the like in the early 90'ties...
All formats have either been improvments on older formats, or been created by companies to make money/control music business... (Like .wma)