I came upon Pandora by accident from delicious, and I'm still figuring out what it is, but so far its been a great place to find new music. Enter one song or artist and the Music Genome Project will match characteristics of that song and suggest other songs, then play the entire song inside the player (!). You can give it a thumbs up or thumbs down, and it suggests more songs based on your feedback. I'm currently on a garage/math/prog hayride based on my original Rodan selection. Many of the bands I know but the ones they suggest that I don't know fit my taste very well.

The site has taken over 10,000 songs and, "analyzed the musical qualities of each song one attribute at a time." It appears they have agreements with the publishers and are partnered with Apple and Amazon. Check it out and let me know what you think.