Does anybody know of any prepaid visa/master card type of card, where they don't actually require your SSN and other personally identifying information?    Are the days of anonymous cards like that completely over?

and I'd never give it out - talk about a security breach!

Sometimes they ask for a name and maybe an address.

So, Joe Baloney, 123 Fake Street, Blowme, Alabama

I agree. It would completely defeat the purpose of buying a gift card for me. I wouldn't do it.

vanilla visa! no activation required...you buy it and it's yours.... a few places will ask for your ID for some ridiculous reason, but otherwise...
you do not have to call and register it, but they are not reloadable. some of the others (greendot mostly, Amex too I think) require that you you activate whether you will be reloading or not.

I am still able to purchase Visa GreenDot cards at the grocery store.  Just pay up to $500 cash, and take it home.  No ID required.