Public Domain and Royalty-Free Music Clips
LooperMan
A variety of royalty-free loops, samples and sounds.
Partners In Rhyme
This site has some free music and loops, but also has music for sale.
http://www.partnersinrhyme.com/pir/free_music_loops.shtml
Free Music Archive
Some of the music here is usable in videos and other productions. Check the licensing on each piece, and make sure that derivative works are permitted.
http://freemusicarchive.org/curator/Video/
Audionautix
This is a nice collection of music in a large variety of genres. Search, preview and download functions on the site are well-designed and easy to use. All of the music is created by Jason Shaw and released under Creative Commons License 3.0 which permits commercial use. You’ll need to provide a link to the website or add the website to your credits. See the website for licensing details.
Incompetech
This is a variety of music in a good variety of tempos and genres. Most music is licensed under the Creative Commons 3.0 license. If you can’t or don’t want to provide attribution, you can pay a very reasonable royalty fee to license the music. See the website for licensing information.
http://incompetech.com/music/royalty-free/music.html
Pond 5 Public Domain Project
Pond 5 is a major supplier of media clips and a good place to sell your own stock footage, images, music and sound effects. But, in addition to the media they have for sale, they have established a section of public domain media that is available for download at no cost. You’ll have to set up a free account to download the clips, but it’s worth the effort. There are some good classical music cuts in the audio section.
Josh Woodward
Josh Woodward has released over 200 of his songs under the Creative Commons 4.0 license. The songs are free to use for most uses with attribution. If you can’t give attribution, you may pay a very reasonable licensing fee. There is both instrumental and vocal music.