Supposedly anonymous.
Until someone in the RIAA starts using it to recover IP addresses and subpoena-ing ISPs, just like they're doing for Kazaa and other P2P networks.

Oh, and if you didn't read the site carefully, you may have missed this:
Blubster is ad-supported software. It is part of the Gator Advertising and Information Network (GAIN), which helps keep software free by delivering messages based on the sites you view.
So who knows what other sort of spy-ware you're installing if you choose to use Blubster.