This should become a list with as many websites offering free music downloads as possible.
Free means that the music on the following sites is free for PERSONAL USE. It CAN also mean that the music is free for non personal use or even free for commercial use, but it doesn't have to mean that, as it varies from site to site.
http://incompetech.com/m/c/royalty-free/ (large database, many different genres and free for non personal and even commercial use if you mention where you got it from)
http://sam-free.com/songs.html (website in Japanese)
http://mymedia.yam.com/Ilan1 (website in Chinese)
http://www.musik-fuer-menschenrechte.de (musicians playing for human rights - website in German - free for personal use)
http://www.superopera.com (huge archive of classical music performed by Alberto Cobo, free for personal use)
http://www.lisztonian.com (free classical music)
http://www.mozart-weltweit.de/mozart00.htm (gigantic Mozart archive)