Your best bet is Creative Commons music, since there are about 350,000 tracks to choose from, all free.
Simply search for Creative Commons "Attribution" music on Vimeo
http://vimeo.com/musicstore and/or at
http://www.jamendo.com/en/ (use "advanced search" to make sure your search results contain only such-licensed tracks).
IF your video is non-commercial, you can also search for Attribution-NonCommercial Creative Commons tracks, which are more numerous and will expand your choices.
The only thing required by a Creative Commons track when used is to give credit (name of the artist, title of the track/album, preferably a link too to where you found it). That's it.