The single most stunning piece in the museum: the Bell X-1, aka "Glamorous Glennis", flown by Chuck Yeager in 1947, and the first flight to really break the sound barrier. There are some other possible cases of the sound barrier being broken during World War 2 by German and British pilots during dives, but none of these included sustained flight over Mach 1.
The Spirit of St. Louis, flown by Charles Lindbergh for his 1927 non-stop transatlantic flight from New York to Paris. In order to have improved center of gravity, the fuel tanks were placed in front of the cockpit - which also meant that no forward facing winshield could be used; Lindbergh navigated primarily from instruments, and a forward facing periscope was also installed.
The Apollo 11 command module capsule! They have it totally sealed off in plexiglass to keep heathens from touching it.
One of my favorite aircraft: the X-15, the grandson of the X-1. Both aircraft were carried while slung under the wing of a modified bomber like a giant bomb (B-29 mothership for the X-1, B-52 for the X-15), to be dropped off at high altitude; this was to conserve fuel which would normally be spent during takeoff. The X-15 not only set speed records at flying nearly 7 times the speed of sound, but also set altitude records, flying up to 100 km and past the Karman Line (i.e., officially into space). The shuttle program used a lot of the information generated by the X-15 later on during the 1970's.
A mockup of the Apollo-Soyuz test project in 1975, which ceremoniously
marked the end of the space race.
A German V-1 'flying bomb' or 'buzz bomb', powered by a pulse jet engine; nearly 10,000 V-1s were fired from occuppied Europe at southeast England in 1944 and 1945.
The big brother of the V-1, the V-2 rocket, a short range liquid-propellant ballistic missile developed in Germany during the second world war. I've seen two of these: this rocket, and one at the British Military Museum in London.
Easily the sexiest aircraft in the museum: the Hughes H-1 racer, which Hughes flew himself and set world speed records in. The film "The Aviator" shows Hughes flying the H-1 during a flight in which he ran out of fuel and crash-landed; it was intended as a prototype and proof-of concept for next generation fighter planes, and Hughes later indicated he felt such military aircraft as the Japanese 'Zero' were ripped off from his plane. One of the innovations for this aircraft were flush rivets.