One of the real finds in my time wasting on the internet this summer, as it rained all August, is Pandora. It was literally the first thing that came up on Stumbleupon, and probably the best thing I have found yet on it.
Pandora Internet Radio - Find New Music, Listen to Free Web Radio
You can get there from the widget on the side of my blog.
All you have to do is enter a choice of song or artist, and the Music Genome project analyses your taste and produces a stream of similar music which you can refine to keep it within your taste. I have discovered lots of new (to me) music with the Astor Piazzola radio station.
After about half an hour it asks you to register, which you can only do with an American zip code. I have been listening happily ever since.
You can order the music you hear from iTunes or Amazon.