My daughter showed me this cool site called Project Playlist (playlist.com). It’s a social networking site based totally around music. You enter an artist in the search list and it comes up with a bunch of hits. You can then add them to your own custom playlist. It appears that many (most?) of the links are to MP3s sitting on various web sites. This isn’t something like Pandora or Slacker, where you aren’t in full control of what’s playing. You can even get the URL of the file so you could download the file if you wanted.
You can also add the player to your website as I have done on Offbe.at. They seem to have a pretty good library and was able to find some obscure stuff, but not everything. Check it out and enjoy while its still around ;-)