Try to catch some sleep on the flight. Try using a neck pillow, eye mask and earplugs and see if any of these can help you nap. Most of us get sick when we are stressed or tired. If you can learn to sleep on the plane, you might be able to stave off a little of that exhaustion.
Bring a scarf or a small blanket. Who wants to wrap up in a stranger's blanket? Ick! Ick!
Wash your hands as often as you can. Be sure to get warm water and soap on your hands. Some studies show increased levels of bacteria in water that comes out of the spigot in the airplane bathrooms, so if you're worried about that, carry a hand sanitizer and use it after you wash all the dirt off your hands.
Keep your regular schedule when you travel. Eat the same breakfast, work out the same amount and avoid all the excesses that travel can bring. It's boring advice, but it works.
Get a massage. Some studies show that massage can help to boost your immunity. De-stressing can't be bad, and massage is one of those remedies worth making time for.