quote: "Out of curiosity, have there been any air accidents where the final cause determined was that the flight crew had fallen asleep?"
Capt Scooby, I'm sure you just penned the question quickly and didn't give it much thought. Had you given it more thought you have realised that "falling asleep" is a symtom of chronic fatigue. We are just talking about plain old moderate fatigue. The kind which causes you to make "errors" as opposed to "falling asleep". The kind of errors that make you mis set altimeters and fly into the ground a few miles before the runway.
There are plenty of accidents out there which fit this category. Very hard to pinpoint fatigue as the "cause" but easy to realise it was a contributing factor to the accident. If you remove a contributing factor then it could be argued that the accident may not have happened. All very speculative, but either way, fatigue is a very very very bad thing to have in the flight deck.