http://www.pandora.com/

Just checked this out.  You enter artist/songs you like to create a customer station. It then uses the music genome project to select additional music you may like.  You can also continue add feed to tweak it.

I started by adding just three artists to my first stations-- "The Waybacks",  "Hot Club of Cowtown", and "Railroad Earth".  So far I've liked everything they've played.

You can subscribe with a modest fee or play for free and there are supposed to be ads but the must be few and far between because I haven't heard one yet.

Yeah, I signed up for this, but they didn't charge for it. Seems like it's good, but it's supposed to play similar artists to the one you select, but it seems like as the thing goes along, it gets farther from what you started with.

I found that when I gave it more artists, it tended to favor the ones I recently added more than the earlier ones.  I really only gave it a few hours while I was cleaning my office before the holiday break.

My fear about it is I think somewhat true.  This thing is doing a unique realtime stream for every user.  That means bandwidth.  I think they skimp on the fidelity.  I noticed relatively poor sound quality, even for an internet feed.  I'll use it once in a while and then switch if I get listening fatigue.