The Live Music Archive is a part of the Internet Archive. From their web page:
The Internet Archive has teamed up with etree.org to preserve and archive as many live concerts as possible for current and future generations to enjoy.
One of the problems, though is that there are just too many bands to choose from. The archive provides streaming mp3s for most bands so you can quickly preview a band to see if you like it, but even then, there are simply too many choices out there. If you don't have a ballpark idea of what you want to hear, you'll just end up lost.
LaMAR will redirect you to a random show in the archive -- all you have to do is click on the "Stream Show" link once you're there.