There is so much to say about this topic.
I travel a lot and am of the opinion that all US carriers are bad and so are most international carriers. If you can manage to fly business class ($, miles, or other) it will be a much better experience. If you can't, at least do yourself a favor and pay the extortion fee to get a seat with extra leg room.
Take some form of entertainment for the first part of the flight (music, movies, books, etc.). My system (which will not work for everyone) is to have wine with my meal, a double cognac after the meal, 3 mg of melatonin, contacts come out (IMPORTANT!), ear plugs go in, eye shades on and then sleep. Sometimes, I manage to even sleep through breakfast. I arrive fairly rested and ready to go. Remember to drink plenty of water during the flight (never from the bathroom sink). If you can follow this system, you end up with a relatively short amount of dead time.
Read up on deep vein thrombosis. That is the reason that some docs will be reluctant to prescribe sleeping pills. An advantage of melatonin is that it helps to reset your body clock. As a sleep aid, melatonin does not work for everyone. It doesn't do a thing for my wife. Talk to your doctor before trying it. Also, try it before your trip so you know what to expect. If it doesn't perform as expected, find something else. If you don't sleep, it will be like pulling an all-nighter in college. Remember how you felt after one of those? You don't want to start your hunt like that.
In December 2011, flying back from Frankfurt, I sat next to a nice guy who was coming back from Afghanistan. Unfortunately, unlike bluey's friend, instead of drooling all over himself, this poor guy barfed all over himself, the seat, the blanket, etc.
When I finally woke up, the flight attendant politely suggested that I might want to move to a different seat. Needless to say, I didn't get a good night's rest on that flight. ;-)