I first got my Oyster Card in early 2004. I've long since worried about the privacy issues involved. I've since tried to get an unregistered card, with varying success and found some weird procedural things that mean you end up giving away your personal details to TfL, even though you're using an unregistered card. Finding very few verifiable facts on the Internet, I decided to (formally) ask TfL about it.
Anyway, it's all written up on the OysterCard wiki page, and the TfL request/response information is at OysterCardRFI. If you use Oyster, it's an interesting read.