Protect your nasal membranes from dry air.
Nasal mists and saline nasal sprays have been found to be effective in boosting your body's own system of germ eradication, which works to flush germs from your nose. There's even a product developed especially for this purpose called Flight Mist, but any nasal mist or spray will work fine. Some people swear by the technique of applying a small amount of Neosporin or Vaseline just inside the nostrils (use a Q-tip if your hands aren't freshly washed). Experts say the antibacterial action of Neosporin is unlikely to present much of a barrier when used in this way, but it never hurts to moisturize the inside of the nose.
Hot drinks are also a good way to keep your protective mucous membranes working; they trigger your nasal passages to release moisture and also provide direct moisture as you inhale the steam. Remember, though, that coffee is mildly dehydrating, since caffeine is a diuretic. (Recent studies show the antioxidants in tea offset the caffeine's dehydrating action.) So ask for tea or hot chocolate, or carry your own tea bags and just ask for hot water.
Don't touch the seat pocket in front of you.
Of course it's the handiest place to stash your stuff, but think about it: Previous passengers have put everything and anything in there, from used tissues to dirty diapers. According to the National Institute of Allergy and Infectious Diseases, rhinoviruses -- the primary culprits behind the common cold -- can live up to three hours on any surface, whether that's your armrest, your tray table, or the seat pocket the passenger before you put his tissues in. Keep your books, magazines, reading glasses, and other personal items in your carry-on, if possible. If that's not practical, slide your sleeves over your hands before reaching into the seat pocket.
Disinfect any surfaces you touch.
Using an alcohol-based disinfection product is a good second choice when you can't wash your hands. You can also use disinfecting wipes to wash down surfaces you can't avoid touching. Carry a pack of disinfectant wipes in your travel bag and wipe down armrests, tray tables, and the seat back in front of you.