Well, not completely free of course, but as Creative Commons states it: “flexible copyright licenses for creative works.” Meaning a lot of work from people like you and me (and more talented) that want to share their work with others. If the material you downloaded is just for personal use then it is mostly free (but please donate if you respect the artist). Are you going to use the material commercially, then expect to pay a small fee. A great initiative that is already embraced by quite some artists (I strongly encourage you to have a look for yourself on the website of Creative Commons).
Jamendo is another site that provides only music albums from mainly artists from France and Belgium. They do this by using the licenses of Creative commons. Every album you will find here can be downloaded via the edonkey p2p-network (also licensed via the CC license) or via a bittorrent link (both legal as long you will respect the CC license). All albums can be listened to by streaming audio and I may say: it has very good quality and is fun to do so. With help of the tags it becomes even easier and more fun to find the music albums of your preference(s).
To name a few artists I came up with after browsing for an hour:
An easy to listen to album in the genre vocal/folk is Guillo (France). If you are more into Electronic then you could give Bep (France) a try. Still on the electronic move but mixed with some classical influences and sometimes a bit experimental is Collectif Terra Incognita (France). And for the one that liked the soundtrack of Amelie Poulain (Yann Tiersen), then you should try the classical (piano) album of Ehma (Belgium). If you are looking for instrumental and poetic music, you should give Le Collectif Unifie de la Crecelle (France) a try. And if you are really into experimental jazzy music (lots of saxophone), you have to try TheLinks (Switzerland).
And last but not least, my personal favorite is MAIS 69 (France). A mix of funk, modern jazz, ska and some blues.
To conclude; quite refreshing and away from all the mainstream music from nowadays!