Number one, take a large bottle of water. This cannot be stressed enough. Dehydration while you're traveling is common, and since you only get a drink once or twice on your flight, there will be times when you are more than grateful for that water.
Take snacks that are non-perishable, or even take a small cooler on the plane with you if your trip isn't too long. If you have any blood sugar issues, snacks are a must and there are many healthy ones that are available, like various nuts, trail mix, dried fruit, etc.
Don't count on stopping for food or personal items at the airport. Many times, flights take an unexpected turn and you have to be prepared that you may not have time to grab it. If you think you need something, pack it before you get to the airport, then do a mental check. You can grab anything else you need at the airport before you board.
Take a nice, big fluffy jacket that will keep you warm and serve as a nice pillow. Better yet, pack a small throw. There are also things like travel pillows and other items that make your trip as comfortable as possible.
Take wipes. These can serve as a quick refresher and keep your hands and face clean and germ free. There are wipes available for both hands and face, so be sure to check them out.
Earplugs! These are a must if you are on a long flight, or even a short one. They can block screaming children, crying babies, and everything in between. Foam earplugs are the best choice as you can still block the noise but hear landing instructions in case of an emergency or connecting flight changes.
Get a sleeping mask. This cannot be emphasized enough. A good sleeping mask can make all the difference when you need some good shut-eye on the plane. The mask blocks out light, so that your neighbor can read without annoying you or disrupting your sleep. If you travel first class, many times they supply these items, but you're better off making sure you have them before you get on the plane.