Um, I think it was called Napster and it went out of business several years ago
It seems that you can get away with uploading effectively pirate material to YouTube, presumably because it's considerably lower quality than the retail equivalent (DVD). But of course pirate audio is pretty much identical to the retail product. So I don't think anyone can get away with that in this day and age.
However, I have heard that use of up to 15 sec of audio material does not count for copyright infringement purposes. So maybe there's a market for a YouTube-style site for tiny audio clips?