"in particular, Facebook and Twitter"
Well, colour me surprised.
At least, in Amazon's favour, they hold your bank card info themselves (and thus do not ask for it) and they demand confirmation of this if shipping to a new address, and for viewing information about my account I need to log in (SSL). So it is pretty safe. Without, you can see my search history (frequently edited, as it affects the auto-suggestions) and my wish list, which is full of astonishigly interesting things like manga and "learn katakana in 30,000 days", that sort of stuff. Woo.
By the way, while I notice eBay on the list, I was quite surprised to see PayPal omitted.