Pandora is a site that recommends music based on suggestions (pointed out to me by Matt). But rather than a person-person collaborative filtering approach (e.g. http://www.last.fm/user/tristanf/) it seems to be based on a very detailed genre-based approach.
"Over the past 5 years, we've carefully listened to the songs of over 10,000 different artists - ranging from popular to obscure - and analyzed the musical qualities of each song one attribute at a time.".
So I set it up with John Coltrane and it started playing tracks like those shown below...and, yes, they were pretty 'Trane-like. (Link)
Blue Rose by Donald Harrison because "Based on what you've told us so far, we're playing this track because it features block chords, a piano solo, aggressive drumming, a driving swing feel and a groove oriented approach."
Bye George by Michael Brecker because "it features tenor sax head, aggressive drumming, a groove oriented approach..."
Or starting with Common gave me tracks with "east coast rap influences, R&B influences, a knack for catchy hooks, headnodic beats and use of call & response vocals." Link
I'd love to see the classification system and it would be nice to be able to navigate by this - e.g. show me more tracks with a piano solo and a heavy use of chordal patterning (!). Have a go - but note that after 10 hours of music you have to start paying.