Twice had it happen to me coming back from the west coast to the east (I think both were from SEA, one in to ORD, one in to DTW) and while I don't remember all the circumstances, both were some kind of flight delay/mix up/late flight that arrived at like between 2 and 3 a.m. I was rebooked on my connecting flight in the morning at 6:30 or 7 so who's going to get a hotel for a few hours. Both cases, I scouted for seating that didn't have arms, found 'em, stretched out and snoozed a few hours till people started showing up.

The spend a (my timezone) night in an airport was last year, DTW to AMS where it was the earlier of the 3 evening flights on NW, they had a great tailwind and arrived at like 5 am instead of 5:55. Thats only 11 pm in eastern time zone. The flight I was connecting to didn't leave till 1:30 AMS time so I went to the upper level and sacked out on those great lounge chairs in the "quiet" area. Met up with people from the office back home when I got to the final destination. They had traveled on different flights but the same overnight run, I was fine after nearly 6 hrs of sleep at my normal time, they were wiped out.