One of the best free sites is Noisetrade.com. With Noisetrade the artists directly make there music available for free downloads. If you like what you hear you have the option of leaving a tip.
Bandcamp.com isn't exactly a free site because the artists names the price, but some artists do make free downloads available. Others make the download available for name your price, is could include free. Both Bandcamp and Noisetrade allows you to stream entire albums and song for free which is an added bonus.
Another good site is Daytrotter, but it is no longer free (even though streaming is free). But it only costs two dollars a month and you get unlimited downloads. Basically the artists record sessions for Daytrotter and these sessions are available for download. This includes many of the better known indie artists such as Bon Iver, Wilco, Iron & Wine, The Civil Wars, Moby, etc...
One other free resource I have used from time to time is the free music archive (http://freemusicarchive.org/). All of the songs are made available through a creative common license, through different curators.