Jamendo Music: Ad-free downloads and offline playback.Advanced Download Manager: Best for quick downloads.SoundCloud: Best for quality and quantity.Audials Play: Perfect for radio recording.There are tons of free downloadable music content on pirate sites that are guaranteed to be illegal, so ensure that you have Creative Commons or Copyleft permission before downloading any MP3s.
However, you should remember that just because something's available as a free music download, this does not equate to it being legal as the owner of the song might not have given permission to the site to do so. These apps allow you to download songs (if they carry those tunes) for free.