Originally Posted by DennisW+1 to this. I stupidly dropped my 4-day old iPad2 on to a hardwood floor and shattered the screen. I went to the local Apple store after reading these stories and just asked to have it fixed. They told me the same, "one time only, I've never done anything like this before" and gave me a brand new one at no charge. I'm sure by now the store employees know that the work is spreading on the internet about this unofficial policy, but they have to play the game.
So, as Tim said, be humble, polite, and thank them for this favor. I even popped for the Apple Care plan after that just as a way of saying "thanks".
And I might add that some sort of protective sleeve or folio is a wise investment, as you won't get a second free replacement. Apple prices the cost of a screen replacement at $300, BTW.