A coworker sent me a link to Pandora "a music discovery service designed to help you find and enjoy music that you'll love." The service is based on the work of the ambitious members of The Music Genome Project (MGP) who, according the website, spent the past five years listening to and analyzing the music of over 10,000 artists, quantifying "everything from melody, harmony and rhythm, to instrumentation, orchestration, arrangement, lyrics, and of course the rich world of singing and vocal harmony."
I haven't found a new favorite band yet, and I definitely don't like all of the music they've suggested, but it has a lot to recommend it. First off, it's free! There's also a subscription if you want to avoid ads, but so far they're quite unobtrusive. Maybe if enough people buy music (from Amazon or iTunes) through the service, it'll stay that way. Also, their player uses Flash, so you don't have to download some proprietary media player or get stuck with something awful like... Real.
You start by creating a "station", seeding it with the name of a song or artist you like. The player then plays what it considers a "typical" song by that artist, followed by those it considers to be similar. You can click on a song to get various options. Why did you play this song? gives you insight into how the MGP catorized songs. If you like the song, you can add it to your Favorites list, which can be printed and also includes links for buying the song from iTunes or Amazon. Finally, you can give the song a thumbs up or thumbs down to govern whether Pandora should play it again in the future.
You can have up to 100 stations and you can share them with others by clicking on the down arrow at its right end and selecting e-mail this station to a friend. I haven't tested it yet, but presumably you can e-mail them to non-friends too. ;P
Check it out!