Most flights, that's a big no. Even when I really, really want to sleep.
The one time I did sleep was so frustrating. A few years ago, I was laid over in LAX for a delayed 5-hour flight back home. As I waited for the projected 10pm boarding, I watched a young man with his girlfriend make a huge scene with the flight attendants at the gate desk. I've no idea what exactly happened, but 30 minutes later they called me over and offered me the last first class ticket on the plane. When I said I couldn't afford it, they said it was for no additional charge. Turns out, the young man from earlier was in first class and his girlfriend was in coach (and not too happily, btw). I assumed that I became a pawn in a lesson learned that evening. Anyway, the one time I was in first class for a five hour flight ... it had to be in the middle of the night and I slept through it. <sigh>