I did not have to give my Social Security number to use my current phone.Apple does not need that information.
This isn't specific to the iPhone. Apple has nothing to do with your SSN. AT&T is requiring it for activation. Cell phone carriers always require SSN's when signing up for a contract. Since the only option AT&T is offering for buying an iPhone at launch is to sign up for a two-year contract and get the phone activated in the store (not an uncommon practice for hot new phones) it makes sense that you would have to provide an SSN at the Apple Store.