A friend and I were talking today, and this was a question that came up. He has fallen asleep in a couple of places over the years, as have I. Inside the parks, I once slept on an MGM bench for a couple of hours. I was really tired! Outside the parks, I visited WDW with my class trip in 1984, and ended up falling asleep on a hammock at the Polynesian - also for a couple of hours. Not a big deal normally, except that I ended up with a massive sunburn that sent me into shock at the airport that evening. I have very fair skin, and used baby oil - not realizing I'd end up cooking myself.
That is actually all I can recall for myself right now.