If you know of a site not listed in this post, let me know and I'll add the link!
Give Life Back To Music
Public domain, free music. Various types and genres.
Any list of free music sites would be remiss without a mention of Kevin MacLeod's vast database. Music on Incompetech is all instrumental and is searchable by genre, mood and feel. A great deal of it is specifically geared towards game or soundtrack use.
The Kyoto Connection
Japanese style pop and contemplative, also available in album-size .zips.
Dig CC Mixer
Offers tracks with vocals and instrumentals. Something that seems unique to this database is the offering of several tracks with their component parts- you'll be given the option to download the instrumentals only (on a track with vocals), just the drumline, just the bass, etc. You can also search by the type of media you want to use the music in (video, game, podcast, etc). Most of the music seems to be electronica.
Free Music Archive
FMA offers a wide variety of music in different genres; my one complaint is that the site doesn't allow you to search by license, or mark tracks as licensed for commerical use or not licensed for commerical use. I prefer to stick to music that's been okayed for commerical use even if I'm not intending to sell the project I'm using it in, since the line between commercial and non-commerical can be a little vague.
SoundClick does allow searching by license and you can see at a glance whether or not a track is okayed for commerical use. There's some darn good music here too, vocal and instrumental. There's also a wealth of music you can pay to license for commerical use if the free stuff just does not work for your project.