1. Figure out what they need to sleep. Every kid has her unique sleep needs, and finding a way to meet them will ensure your kid doesn't pick up the most viral strain of the most viral cold going around the day after arrival.
My daughter is a bit of a challenge - she NEEDS darkness. Figuring that out was the first trick. Creating darkness on an afternoon Europe to USA flight (10h of brightness!) was the next. Voila! The 2-blanket-cave.
And (this should go without saying), for the love of all things good, if your kid has a favorite sleep lovey, or a blankey or whatever, make sure that thing is in the carry-on!
2. DVD player. And child appropriate headphones.
Our kids don't get to watch too much TV and it turns out their appetite for TV is only 2h long, although on a long flight that cycles. It also turns out the TV can be quite lulling ... think of how many adults you know who snooze by the flickering lights. Not all airplanes have a children's channel or the one they have may be more suited to 7 year olds than 3 year olds, so your own portable DVD player is a must. Or an i-pad loaded with movies. You get the picture. The headphones are a must not only to avoid broadcasting Sponge Bob to your fellow passengers, but also for tiny heads the adult 'phones fall right off and many child styles have a feature that prevents the sound from going over so many decibels - necessary when your kid loves to play with all the buttons.
3. Snacks & treats.
To ensure your kid actually eats something - because so many are so picky - bring food you know they will eat. As travel day is special and you'll do anything to get them through it, bring a few special treats too. Sometimes what your kid considers a treat isn't even particularly unhealthy (think yogurt covered raisins).
4. A new book that your kid chooses (you can get one in the airport, most bookstores have an English section. Or however else you obtain your books, but let it be chosen by your kid and never read yet). AND a favorite book.
Kids can read the same story a dozen times in a row. A new book easily can be read 2 dozen times - same for the most favorite. You may want to tear your eyeballs out, but your kid is happy and quiet and cute to the fellow passengers when saying "Again!" for the 20th time.
5. A bunch of small wrapped "presents".
I threw this one in as lots of people suggest it. It never really worked with my kid (although we'll try it with #2 soon!). Wrap up small toys, the special treats you brought, a new box of crayons, whatever it is. Some suggest having one for each hour of the flight and letting the kid open one each hour. For my kid the novelty wore off after a few hours and she was eventually busy sleeping (see #1!) but my motto with the kids is it's better to have too much than not enough.
6. Extra clothes.
For babies it's a "duh". Same for potty trainers. But other wee ones too can have an unusual reaction to particular turbulence. Or, for example, my daughter used to puke when the plane got too hot. Or they spill their juice. The number of reasons you might want new clothes for your kid are innumerable and let's face it, kids' clothes just aren't that big. At worst you have spare clothes for when the airlines loses your luggage.
7. The airline will provide this one for you ... an extra blanket that you can put down on the floor before letting your little ones play on their "picnic blanket" under their seat.
Kids get claustrophobic in their little seat. They generally don't like their motion restricted anyway. The floor had less real space, but it's relatively forbidden so it's cool and if you put the blanket down first it isn't so disgusting ... and it gives them room to spread out.
8. Glue stick.
So many uses! One thing we do is go through the in-flight magazine and/or the airMall flyer looking for ... animals/red things/pretty dresses/whatever. That's quality entertainment in itself. Then, you can tear them out (kids love to rip paper!) and glue them to the airsick bag. It's a good hour of entertainment. Those bags are pretty sturdy, depending on how much glue you use you can tear your initial masterpiece off the bag and go back with a new theme later.
9. Color Wonder.
4 colors and one new book will get all the attention your kid has to give any one thing. If you can't get your hands on these, use crayons and a new coloring book and once you're in the USA, head to the nearest kids' store and get some. Stock up!
10. Whatever packable, non-breakable things they like to play with.
Sort of a duh but look around the playroom and hide away a few things about a week in advance so they are fresher and newer on travel day.
10. What NOT to bring.
Puzzles, balls, Legos, play-doh unless you are absolutely certain it won't end up ground into the fabric of the chair, anything you'd be sad to lose (except of course the sleep lovey, that one's a necessity).