When it comes to giving out a phone number or zip code, I make one up on the spot. When I had to register for a new supermarket discount card, none of the information I gave was real - fake name, age, phone number and address (the address, if it existed, would have been in the middle of a river). Of course those discount cards aren't used to cash checks or tap into a bank account, so in the case of the Target card, I'd have to weigh the benefits over the loss of privacy. I've shopped at Target maybe twice in the last five years, so the benefits are minimal for me. If a simple discount card application asked for my SS or a state ID for verification, I'd decline the card altogether.