Given that the gamecenter password is the same as your iTunes / Apple account password, they could wipe out your account balance by buying / renting things. If

Given that the gamecenter password is the same as your iTunes / Apple account password, they could wipe out your account balance by buying / renting things. If you have any card details stored then they could go onto the Apple Store and order using those. They could see your billing address, and so intercept your mail, thus gaining more documents to eventually steal your identity. Of course, if you only buy using the pre-paid cards you can buy in retail stores then all they can do is wipe out the balance. I'm sure your response was partly flippant, but the implications because of Apples one universal account means that someone determined could do a lot of things.