If you're looking to download music, torrents are probably the way to go. Just get a torrent client like utorrent by searching on Google, then search for torrents and anything you want to download. Obviously the legality of what you're downloading will vary.
If you're just after something to listen to on your computer, though, a site like grooveshark allows you to listen to pretty much any track you can think of, and also searches out tracks others have liked based on your preferences. This also has the advantage of being completely legal, and free (so long as you stick to the basic account).