I always had trouble sleeping on flights - or anywhere but a nice, quiet bed. So, after a hellish 24-hour journey home from Australia, I finally called my doctor and asked for help.
There are a number of sleeping pills that can solve the problem. While they don't completely knock me out, they do get me relaxed enough that I can fall asleep. On another trip, I was extremely glad that my MD had given me a small prescription for valium. I offered to pay for the divorce lawyers for the couple sitting next to me, rather than killing them. Without the valium, it would have been quite a mess.
So, if you're going on a long flight, and have the overnight-time to sleep, I strongly recommend seeing your doctor and asking for some sleeping pills. The rest makes the destination so much better!
Also, I agree wholeheartedly with heyoka - avoid alcohol when flying. Always.
1. The airlines do not provide any humidification whatsoever, and alcohol increases dehydration.
2. Alcohol, while sometimes helping people fall asleep initially, produces a much lighter, less restful sleep.
3. Air rage is increased by alcohol. And any normal person will become enraged without any alcohol at all after spending enough time on airlines. No one likes being a cattle. While I encourage air rage wherever I can (it's the only way to get airlines to improve conditions), it will get you arrested and charged with federal crimes.
Finally, hydrate, hydrate, hydrate. In addition to drinking 8 oz. of water for every hour in flight (I usually drink more, but that is the minimum - and yes, you'll have to bring your own water), I use face and hand moisturizer.
The best "secret weapon" I've found so far for hydrating is nasal saline. Simple salt water that you put in your nose. It works like this: When the sinuses dry out, they become much more susceptible to infection. At least one person on the airplane has a cold or flu. More likely, everyone on the plane but you is contagious. Hydrating the nasal cavities helps significantly reduce the risk of infection. (Also, wash your hands frequently and avoid touching the nose or eyes.) (And definitely no unprotected sex with strangers in the bathroom.)