There are increasing numbers of places for on-demand music on the web, like Spotify, Pandora and Deezer. These all let you listen to streaming music over the net, but are no good if you're disconnected. Illegally downloading music to your library is not difficult, but I want to look at legal ways of downloading free music.
The first thing I have to point out is that you have to have an open mind when it comes to legal free MP3s. You probably won't get complete albums, and your favorite artists probably don't give their songs away for free. However, if you're willing to experiment and trust the judgment of good bloggers, there's a ton of free music out there.
Two great sites for free legal downloads are Last.fm and Spinner.com. If you sign up to Last.fm and install their app, you can get free MP3 recommendations based on your listening habits, which is pretty cool. Check out their free MP3s here. Spinner is more of a magazine, but has tons of MP3s you can browse here.
My favorite resource is The Hype Machine, which sources reputable music blogs that host MP3s. These are often MP3s released to promote new albums or groups. You can listen to music on The Hype Machine site, or go to the source blog and download the MP3. There are tons of great blogs listed in their directory, which gives you a massive source of great free music. After a while you'll find blogs that share your tastes, and have a regular source of great new music.