This article in USAToday By Harriet Baskas talks about this problem.
Below are a few excellent quotes from the article.
No matter what your pilot tells you, taking a plane trip these days could be irritating, uncomfortable and even maddening. For millions of people, it also is absolutely frightening. Despite statistics that show flying is one of the safest modes of travel, many people will only fly if they must. Others are so afraid of flying that they will never travel by air. And when people are too afraid to fly, they can ground not only themselves, but their families, their vacations and their careers. For years, Maria Smyth, 42, was one of those truly fearful fliers.
Fortunately, she found free monthly classes at the Phoenix airport. Taught by Ron Nielsen, a veteran airline pilot with a master's degree in counseling, the Cleared 4 Takeoff seminar is similar to various programs around the country. First, participants are encouraged to identify and talk about what scares them. "We educate people about flying and airplanes," Nielsen says. "We identify the noises and point out that most of them are routine."
In the past, many airlines offered their own fear-of-flying programs. Pan Am may have been the first, with a program that started back in 1975. Over the years, classes were offered by American Airlines, US Airways and Northwest Airlines (the WINGS programs), but like other passenger services, programs offered by domestic carriers have been dropped. Several international carriers still offer them. In Australia, a course offered in association with Qantas Airways includes classes, tours and a Qantas flight. In the U.K., Virgin Atlantic's one-day Flying Without Fear classes include 2000 Virgin Airmiles, a hot meal, a relaxation CD, insurance, a 45-minute flight and a certificate of achievement signed by Richard Branson.
Nielsen with the Cleared 4 Takeoff classes in Phoenix says that although air travel is definitely becoming more stressful, it's not really the long lines at the airport, the Transportation Security Administration or the threat of terrorism that makes people afraid to fly. Rather, "those are the triggers that release these little time bombs inside people who are already afraid to fly."