Music: For my demo reel, I used a popular song without permission (Beastie Boys) because the reel revolves around a music video that I did for a Beastie Boys contest... So far I haven't had any legal issues, but I could technically be asked to remove the music if the record label felt so inclined and was aware of it's existence. I could even be sued, but it's unlikely.
It's a chance you take. You can license some decent music pretty cheap at http://www.pumpaudio.com. The best part about that music is it's by indie bands and is much better sounding than cheesy stock audio.
Or, even better, get a local or indie band to let you use their music in exchange for free publicity. Mention the bands name and website before or after the reel, and you could be widening their audience for them. Do you have any friends in a decent band? That's the best place to start.