While it's a fundamentally different approach -- Pandora has the Beatles.
I've been a Pandora One subscriber (no ads for $30/year) and I'm quite happy with it. Sometimes I do want _A_ song, but in general, outsourcing my playlist to their algorithms has worked out great.
Right now, I use a combination of Rhapsody and Google Music to get The Beatles (from CDs I own and have ripped.)