GrooveShark is an interesting free service that allows you to search for music (artist, song, album), stream it directly and even create playlists from your computer.
GrooveFish itself is an excellent application. Visually it matches GrooveShark and is quite pleasant to look at and furthermore it works very well (audio fidelity is way better than Pandora). It's simple: search, select and play. Heck, it'll even auto-pause on a phone call or when you remove your headset. Ability to create playlists and save favorites is coming in future versions.
But the big issue here is of course U.S. copyright law and GrooveShark: this is not just streaming a ShoutCast station but rather allowing you to stream on demand any song/album/playlist you create, which is a bit sketchy, legally speaking. To their credit they do have a way to notify them of DMCA violations and they will comply. But as this service becomes more and more widely known, you can bet you'll start to see your favorite tunes cooperatively pulled down from the site.
In other words, enjoy it while it lasts.