Through The Lens pointed to Spotify, which is a an online "radio" service which seems to work even better than Pandora. You can choose music and sequence, and it does not seem to be limited to some countries unlike Pandora (last I checked). I wonder how they got around all those legal barriers? Or if they really have. For a while there I could use Pandora in UK, but that was blocked later.
So far, I'm impressed. Right now I'm listening to a CD I'd heard about but never had a chance to hear, a 1994 collection of covers of songs of one of favorite Danish bands in the seventies. I'd never expected to find a reasonably rare Danish item in a second after my first search.
Update: it seems that Spotify, refreshingly, is started in Europe or UK. And not yet available in North America. See comments for more info.