I got introduced to this internet 'radio' a few weeks ago: www.pandora.com. You go set up an account, you can then create your own radio stations by typing in an artist's name. Pandora will then create a song list according to what it believes is the genre of the artist you put in and play them. I have so far created 3 stations and it found a number of new artists that I've never heard of before whose music I like. A small negative is that the playlist is not that big, so after a while it starts to repeat; but I guess I can always create another new station.
See what you think.