Everybody knows about Pandora, right? If not, you should really check it out. It's a "radio station" that finds music that is similar to music you already like. As they continue to add features that enhance your ability to direct the flow of any given "station," and, critically, they add lots more music to Pandora's database, it's becoming my go-to music player at work.
On a similar principle, I suppose, is The Filter. I haven't tried this yet because it's not available for Mac, but it promises to dynamically build playlists of similar music out of your own iTunes library. There's some buzz about this little app, but, oddly, no wikipedia entry... for some people, that means it might as well not even exist!
It's unclear to me how The Filter works. One thing I like about Pandora, by contrast, is that they are very up front about and proud of the underlying idea of the software, which is the Music Genome Project. Rather than somehow mathematically analyzing music for similarities (which will someday be possible), they use our existing, semantic descriptions of music to relate various songs.
Lastly, operating on no principle I can discern, is Musicovery, which definitely has the most interesting-looking interface. It occurs to me--as I see the same few bands come up again and again on Musicovery--that even if these applications are built on some sort of sound principle, the actual results could easily and invisibly manipulated to promote certain record labels. Payola is illegal, but payola-with-a-lowercase-p could be pretty rampant on the net.
UPDATE: I fixed the links. Also, from the comments, Lisa B points us to another interesting internet music thingamajig, Last.fm.
Inscribed by Jason at 9:38 AM