I once overslept and missed my NYC -> Australia flight on a dirt cheap lowest-of-the-low economy Qantas ticket. Called them up, fearing the worst, and think I was going to have to pay crazy sums to fly out the next day by buying a last minute ticket.

Because I was calling at a weird hour, my call got routed to Qantas in Australia. Guy answers, I tell him in a panic about my situation and he's like "Yeah, no worries mate. Changed your ticket to tomorrow. How's New York? OMG! Have you seen the Statue of Liberty?!" Ha!