Yes, you can do this.
I just finally got on the bandwagon with Pandora Radio (www.pandora.com). This is a totally cool web based music radio station that you literally create yourself. You are able to choose songs or artists that you like, and a 'station' resembling a continuous playlist will play tunes from the artists you select as well as tunes that have similar characteristics. As each song plays, you can give it the tumbs up to keep it in rotation on your station or the thumbs down to ban it from the playlist. Presumably, as time goes on, your station will get better and better as the computer hones in on what music exactly suits your taste.
This is my first day using it, but it is super cool and is playing a bunch of stuff that I like. And what was my first station called? 'New Wave Radio' - of course!