One of the displays in the National Museum of the United States Air Force in Dayton, Ohio features the evolution of flight clothing.
According to the Museum:
Through the years, advances in aircraft performance have increased the need for improved aircrew protection from the weather, a lack of oxygen, intense heat or cold, or even violent maneuvers in combat. Also, flying clothing must be flexible enough to allow crew members to perform their various tasks. This exhibit displays representative examples of flight clothing worn by U.S. Air Force crews from the days of the Air Service in World War I to Air Force astronauts flying the Space Shuttle today.
More aviation-related memorabilia:
Air Force Museum: Aviator jackets (photo diary)
Museum of Flight: World War I memorabilia (photo diary)
Museum of Flight: World War II memorabilia (photo diary)
Olympic Flight Museum: Some airplane memorabilia (photo diary)
Olympic Flight Museum: Aviation Uniforms (Photo Diary)
Museums 101: Aviation Memorabilia (Photo Diary)
Evergreen Aviation: Flight helmets (photo diary)