Pandora is a great music site. Tell it which music you like and it plays similar music. For each song Pandora plays you can say whether you like it or not, that makes the selection better and better. You can have up to 100 stations at any one time.
There is an ad-supported version and one where they charge $36 for 12 months of unlimited use. I am trying Pandora and am very impressed by how well it picks music that suits what I requested.

Update May 3, 2007.
Web radio station Pandora is to block most non-US users accessing its service because of licensing constraints. Mounting pressure from record labels has forced the company to stop streaming music to countries where licensing deals have not been agreed.