Somebody on the internet wondering how to get free music. Well, that's something you don't see every day!
All kidding aside, if you want the good stuff (i.e. popular stuff everybody wants and listens to), then to get it legally, it'll cost ya. Amazon, iTunes, and all the usual suspects can help you there. Otherwise, borrow and rip from your friends, etc.
As for the more 'illicit' places to get free music, well, I won't go into that in detail here. But if you must, try a blog aggregator site like this:
Search and Browse Music Blogs - Elbows Music Blog Aggregator.
If you feel somewhat adventurous, lots of sites like mp3.com offer free downloads from emerging and established artists. Amazon also gives away a ton of free mp3's:
Amazon.com: MP3 Songs - $0-$0.01: MP3 Downloads
Another great resource is the Internet Archive. Tons of free downloads of live shows from bands that allow it, most notably the Grateful Dead. Lots of other recordings too, such as Creative Commons-friendly audio, public domain, old time radio, etc.