Special treats: Time to haul out the stuff you might not normally want them to eat but how often do they fly? If they love fruit, terrific, but my experience is that the three Cs (cookies, chips and chocolate) are far more effective as diversions, and sometimes even bribes.
Food: Bring a meal from home if you'll be flying in coach because unless you're heading overseas, the only meal you'll get is one you pay for (and it might not be one your child will eat). Don't forget the napkins and wet wipes either.
Small toys and other diversions: Check out a big box drugstore for cheap, plastic figurines or inexpensive dolls or stuffed toys (I'm talking small stuff here that will fit in a purse or carry-on). There's nothing like a brand new toy to divert the attention of a seat-kicker. Then, haul out the crayons or markers and a pad of paper, pull down the tray table and ask your child to draw the plane (or better yet, a self-portrait on the plane).
Old favorites: A favorite stuffed animal can be a big help for getting kids to nap on the plane, but be careful about bringing a child's very favorite in case it gets misplaced. If you do bring a best buddy, tie a ribbon around the toy's neck with a card that includes your cell phone number. Call it Mr. Sock Monkey's special travel ID.
Don't forget the magic - Part II: Bring a handheld electronic device or laptop loaded with some of the kids' favorite movies or TV shows. Thanks to a recent easing of FAA rules, you'll be able to keep smaller devices on (in airplane mode) throughout the flight on an increasing number of airlines, though laptops must still be stowed during take-off and landing.
On the Plane
Aircraft tours: The days of visiting the cockpit are long over, but you can still sightsee with a trip down the aisle or a visit to the lavatory (for some reason, many kids find the lavatories fascinating). Warning: Do not stroll the aisles during beverage service when you might block a cart (or a harried flight attendant), and do not under any circumstances get out of your seat if the seatbelt sign is on.
Books and games: Most kids love being read to, so be sure your tablet or e-reader is loaded with favorites, and of course, there are always the original hard-coverbooks. Try some nonelectronic games, too. Older kids like trivia, and you can surf any number of sites to load yourself up with questions (try Googling "trivia game questions") or try alphabet games on smaller kids (name your favorite thing that begins with "A" and so on).
At Wit's End
When all else fails: If the kids are really acting up, don't ignore it. Nothing bugs your fellow passengers more than parents who just sit back and let kids go wild. If you look like you're trying to get the situation under control (even if it's not working), people will usually be understanding. Some may even offer to help! But yes, there are times when children cry and there's nothing you can do about it. Do your best to comfort them and take comfort in the thought that the plane trip won't last forever (it'll just seem like it).
Don't forget the magic - Part III: Adults-only magic: Cocktails! Sometimes buying a round of drinks (or snacks) for passengers near you can serve as an apology for kids who haven't taken The Talk to heart. I know some parents who swear by this method, though I've never had occasion to use it.
Ready to fly? Good, and remember, we were all kids once. Do what you can, but don't forget to have fun with your kids. They won't be kids forever.