With Pandora you type in the name of your favorite artist and the site will start streaming a radio station which has songs from that artist and others similar to it to your browser. You may also type in the title of a song if you prefer. No downloads or registration required.
Here is a link to Pandora if you would like to give it a try
http://www.pandora.com
Pandora is one the sites features by Time magazine in their "50 coolest websites." You can read more about those sites with this 5 Star link
50 coolest websites of 2006