Originally Posted by ruckzac

I've only ever heard of airport kiosks asking for a credit card (read: not necessarily the credit card used to make the purchase) as a method of quickly inputting a passenger's name in order to look up their PNR (passenger name record) and ticket.

If you have the record locator, you can check-in online. Otherwise, you can check-in at the counter with a photo ID that matches the name as it appears on the ticket.