Look for music licensed under Creative Commons. Here are some examples:
Free Music Archive: Music available under a number of different licenses. Check the Artist/Album pages for license information.
Free Stock Music: Royalty-free licensed music
Overview of Creative Commons licenses
Articles:
Creative Commons Podcasting Legal Guide: "The Good News: Five Instances Where Permission is Not Required"
Creative Commons Podcasting Legal Guide: "Fair Use Under Copyright Law and Its Application to Podcasts"
"Using copyrighted Music and Media in Your Podcast"
"Trying to Understand Fair Use and Using Music in Podcasts"
Audacity's "Copyright Laws for Bloggers and Podcasters"
Note: The music available via these streaming audio services cannot be used in your podcast. They are for listening/study purposes only. No download is permitted and you are not permitted to publish, broadcast, communicate, or redistribute materials from the services.
The library has a cd music collection located on the second floor between the two halves of the library, across from Special Collections & University Archives.