Your mother was right: You should always keep your hands clean. At least when they're likely to come in contact with objects and surfaces that have been handled by someone who might be coming down with a cold or the flu. Once the germs are on your fingers, you can easily spread them to a vulnerable part of your body, such as your mouth or nose. This is especially true in a crowded environment like an airplane, where a large number of people are packed together in a small space, constantly touching things and breathing recirculated air that has more and more germs in it the longer the plane remains in the low oxygen environment of the stratosphere.
Of course, you can't necessarily excuse yourself to go to the restroom every hour just for a brisk hand washing, so carry a small bottle of commercial hand sanitizer with you, preferably one with a high alcohol content (at least 50 percent). It's specially designed to minimize the risk from germs and it makes your hands smell better in the bargain, too. And because respiratory illnesses are commonly spread by hand to nose contact, keep your hands away from your face -- if at all possible.