http://www.pandora.com
You type in the name of a song or artist and it starts playing songs similar to hatever you put in. I doesn't just play music of the same genre of the one you put in but recognises common themes such as "heavy metal roots", "strong vocals" or "electric guitar rifts". You can rate songs on whether you like it or not, so it gets a better idea for your taste in music and adjusts to play songs that it thinks you'll like more.
You can make up to 100 stations, all of which are separate from each other. After a while (about 10 songs, I think) you have to register. It's free (though there will be an option to pay, which doesn't give any perks yet), it asks for a zip code. If you don';t live in the US, don't worry as it'll accept a random 5-digit number (worked for me anyway).