Check out http://www.pandora.com. Based on an artist or song name, a station is created that plays similar music. A great way to discover new music.

The site is free but requires registration after a number of songs have been played. When you register, you can also mark songs that you like for later reference. The free version has adverts.

Great stuff! At the time of this writing, I am listening to a music station based on Queens of the Stone Age. A lot of bands are played I have never heard of, but it is the same genre. Exactly what I needed!