The musician Moby is offering film music for "independent and non-profit filmmakers, film students, and anyone in need of free music for their independent, non-profit film, video, or short." You need to register to hear the music at mobygratis.com. You must request a license to use the music.
Moby makes techno, dance, ambient, rock and other types of music. His music has been used in all three Bourne films, Cloverfield, Miami Vice, xXx: State of the Union, The Devil Wears Prada, CSI: NY, The Sorpranos, and lots of other stuff.
See this clip from the Sundance channel where Moby explains the website.
You can see a list of short films that use Moby's film music on this YouTube playlist.