I think I'd be quite amused if I woke up sat on the plane and everyone was gone

. But, I'd be worried if someone had been waiting for me at the airport, as surely they'd be in a confused panic about their vanished family member.
I have "done a Ross from Friends" before though as a teenager; fell asleep on my train home in the morning with a hangover, woke up 4 stops (and 50+ miles) past my stop
Also one of my friends fell asleep on a bench in Glasgow Central Station and was woken up 4 hours later by a concerned little old lady

. Its a busy station so I guess it is possible to sleep through a lot of hustle and bustle if you're tired enough!