Just found this web site that list every music artists from every genres (click on Artists On-Demand link). And then it list each artists albums, and every song from each album. Then you can click on the song to listen it.

You can also search a particular song by clicking on Song On-Demand link.

The web site also include multiple radio stations (top of web site) which you can stream.

Music On-Demand - A Better Internet Radio Station on ABetterRadio.com