There are many royalty free music sites out there, and tons of royalty free music on youtube. Just make sure you read the terms and conditions of use, and abide by them. Use some common sense, and when you can link back to the creator of the music. Quite often they will appreciate their music being listened by a larger audience.
Do what I have learned to do, if you are unsure about the music you are wanting to use, or dont know where it came from or who made it, upload it to youtube as a blank video and make it private.. Wait about 10minutes and see if you get a copyright claim on the music you uploaded.
Even if it is copyrighted, in many cases you can still use the music, but you cannot monetize the video...