Ever heard a song that you thought was fantastic and wanted to hear more artists/songs like it? Want new artists recommended to you not based on who bought their albums in combinations with one you liked (a la Amazon), but rather on their musical similarity to your favorites?
Pandora.com has what you've been looking for. Enter an artist and/or song and it will produce a radio station of similar songs based on their intrinsic musical qualities (melody, beat, etc.). As you listen you can improve and tweak the system by saying whether a given song matches what you're looking for.