JFK once: got in to LGA at midnight, had a 7AM departure from JFK. When I got to the airport the last flights of the night (AA terminal) were just claiming bags. I parked up in a quiet corridor, laid out sleeping bag, backpack as a pillow, and alarm clock (cell phone) to wake me before my flight.
No problem sleeping, and the gradually increasing din as people started checking in below me actually beat the alarm clock in waking me up.
I'd do it again if it were intentional, but would probably rent a car and sleep in that if caught unexpectedly, assuming I had the money. Done that several times, my favorite being in MCO's remote parking lot where the security guard actually gave me a wake up call so I wouldn't miss my flight.