A friend (hat-tip J.C.) recently twigged me to Pandora Internet Radio, and I’m glad about that.
You type in a song or performer, and this online web service, part of the Music Genome Project, consults its database of artists and puts together a virtual radio station of similar songs, based on your song’s musical structure, genre, tonality, and the performer’s reputation. The music plays automatically from your web browser.
It’s Googleliciously to use, it’s free, and it doesn’t spam you when you register. My “They Might be Giants” channel is full of surprises, my "Slowdive" channel induces a comfy trance, and my "Sun Ra" channel sets me down gently on another planet.
So far they don’t have much non-English-language music available, but you can apply for a job helping them find and classify French and German pop.