Pandora, the online radio station of the Music Genome Project, is the latest in the wave of personalized web radio. The Music Genome Project was started in 2000 by some music loving technophiles, with the goal to "capture the essence of music at the most fundamental level", categorizing songs by melody, harmony, rhythm, instrumentation, orchestration, arrangement, lyrics, and of course singing and vocal harmony. You provide Pandora (www.pandora.com) with the name of an artist or song, and it constructs a playlist of artists and songs with similar musical characteristics. You can further tweak the playlist by clicking on "thumbs-up" or "thumbs-down" for a particular song, and this way Pandora "learns" what it is you like. Thumbs down songs will be removed from the list and not played again. You can also click on the "why was this song selected" option under the menu button, and it will provide a list of traits that make the song similar to your original artist or song. For instance, on my "Sarah McLachlan" station, Pandora played the song "Gravity" by Sara Bareilles. When I asked why, it said "Based on what you've told us so far, this song was selected because it features mellow rock instrumentation, mild rythmic syncopation, acoustic rhythm piano, acoustic sonority and use of a string ensemble." So there.
Try it yourself. It's easier than last.fm because you don't have to search for and add the artists yourself, and you may find some new artists you didn't know of before.