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Last.fm recently rolled out a new feature: Similar Tracks.  Last.fm will tell you what fans of a particular track are also listening to.  The similar tracks lists are created using the last.fm collaborative filtering algorithm (people who listened to X also listened to Y)  Last.fm seems to filter out all tracks by the same artist as the seed track so you end up with an interesting set of tracks from different artists.  Here's the similar tracks last.fm gives for Hey Jude:

• The Who –  My Generation
• The Rolling Stones – Sympathy for the Devil
• The Who – Pinball Wizard
• The Rolling Stones – Paint It Black
• The Kinks – Lola
• The Kinks – You Really Got Me
• The Animals – House of the Rising Sun
• Creedence Clearwater Revival – Down on the Corner
• Steppenwolf – Magic Carpet Ride
• The Beach Boys – Barbara Ann
• Norman Greenbaum – Spirit in the Sky
• The Hollies – Butterfly
• The Hollies – Rain on the Window
• Manfred Mann – Hymn (From Jupiter)

And for Stairway to Heaven:

1. Queen –  Bohemian Rhapsody
2. Eagles – Hotel California
3. Deep Purple – Smoke on the Water
4. The Doors – Riders on the Storm
5. Aerosmith – Dream On
6. The Who – Pinball Wizard
7. The Who – Won't Get Fooled Again
8. Queen – We Will Rock You
9. Dire Straits – Sultans of Swing
10. The Rolling Stones – Sympathy for the Devil
11. Deep Purple – Child in Time
12. Lynyrd Skynyrd – Free Bird
13. The Rolling Stones – Angie
14. Aerosmith – Walk This Way

It doesn't look like there's any way to play  'similar tracks' radio right now, so you can use the similar tracks lists for exploring but not for playlisting. 

Update:  RJ  points out that the similar tracks data is also available via their webservices.  The similar tracks XML also includes a similarity score that indicates how similar the tracks are.