Hydration, nutrition and exercise will be your best defense. It's a very dry environment and your sinuses will get inflamed, making them a good place for viruses to stick. Drink as much water as you can stand. Also, carry a small bottle of saline nose spray and use it once every flight.
It's tough to eat well on the road, but limit your intake to whole foods. I personally skip meals until I can find a decent meal. Junk food won't help you fend off the funk.
As far as exercise, just walk at very minimum. You have to get blood flowing in order to help the body fight off everything you're exposed to.
You're definitely not alone, but you'll get used to it eventually