All these sites are trying to sell you songs or CDs. But hey, they're letting you listen for free, so seeing an occasionally pitch is okay with me.
Songza: Songza pops up a list from your search on an artist or a specific song. Click to listen and right click to rate the tune, add to a playlist, or send to someone near and dear. One downside: Unless I missed it, there's no way to immediately skip to the next cut.
Jazz Corner: If you're a jazz kinda person, you'll dig Jazz Corner. After a day of listening to their Jukebox, I can honestly say they're in tune with my jazz tastes. I also get a kick out of watching an artist performing and the Jazz Corner has lots to choose from.
Pandora: Another site is Pandora, a site that somehow figures out my musical tastes. Don't believe me? Try it: Head for the site and stick in an artist or group, and see if Pandora doesn't come up with a playlist you like. If it doesn't, and you register, you can reject albums or artists, and you won't hear them again. Alternatively, you can ban a cut for 30 days.
The folks at Pandora have worked hard to make their site easy and fun to use. The interface almost anticipates what you want to do next — rate a song, add music to another station, or bookmark an artist or song.