Pandora.com
Am I the last person in Western Civilization to find out about Pandora.com?
In case the answer to that question is “no,” Pandora is an internet radio service that allows you to create your own “stations” which play music that you like.
You start by picking a song or artist that you like, and then Pandora chooses similar music. As each song plays, you can either give it a “thumbs up” or a “thumbs down”, determining if that specific song and others like it will appear again on your station.
The service is completely free; you just have to register with a username and password in order to save your stations.
I haven’t used it enough to figure out just how good it is at predicting songs that I like, but so far, I’m impressed.