Public domain music includes “a lot of good stuff, especially if you’re a fan of classical, early folk, or early jazz.” Various sites specialize in non-copyright-protected recordings, including Archive.org, LOC.gov/jukebox, IMSLP.org, and FreeMusicArchive.org.
Music blogs, such as Spinner.com and Stereogum.com, often offer artist-supported single-track MP3 downloads. Aggregators of such offerings include HypeM.com, Last.fm, and Ex.fm.
Artist-run sites are another great option. Emerging artists make free uploads available at SoundCloud.com or Bandcamp.com. Established artists and labels make occasional free tracks available too. Consider setting Google Alert to notify you of new releases.
Major digital stores—Amazon.com, iTunes.com—maintain free-music sections where popular tracks occasionally appear.