[saturdaysaint]

MOG does what you're looking for rather nicely - just switch on "MOG Radio" and it provides a Pandora-like station with similar artists.

I liked that but have gravitated to Rdio, which doesn't have that option in its mobile app yet - it's much, much faster (at both search and playback) than any of the other services I used. They recently implemented a Genius function in their (excellent) browser client, so I expect it in their apps soon enough...

[alexophile]

The mobile app does have the "artist radio" function, but there's still some kinks that need to be worked out of it (goes for desktop and mobile)

There's also "recommendations" which I assume uses the same data to provide 1:1 recommendations for new artists based on your recent listening history.