I feel like falling asleep at your computer is a telltale sign that you probably need more sleep. Although it's a bit more understandable if it is a laptop and you're already in bed. I've never had it happen myself, even when up for more than 24 hours. Though I've never stayed up for 4 days in a row, either.
I hope PlutonianEmpire isn't a real pilot, and that if he is, he has a copilot who's less prone to falling asleep while flying planes! I second the "did it crash?" question.
As for the other poll about sleep that's since been closed, I have in fact fallen asleep before. Though you could probably deduce that from the "not staying up for 4 days" part.