The Right Stuff
From The Internet Movie Plane Database
Sam Shepard (Chuck Yeager)
Ed Harris (John Glenn)
Dennis Quaid (Gordon Cooper)
Scott Glenn (Alan Shepard)
Fred Ward (Virgil "Gus" Grissom)
The first aircraft to break the sound barrier, flown by Chuck Yeager. This replica is now on display at the California Science Center in Los Angeles.
This carries the Bell X-1 and X-1A. Played by famed CAF B-29 "FiFi".
Yeager achieves a new speed record of Mach 2 in this.
At the end of the film, Yeager goes for a new speed record in this. The actual plane flown by Yeager in real life was an NF-104A. Three demilitarized versions with an additional 6,000 lbf (27 kN) Rocketdyne LR121/AR-2-NA-1 rocket engine, used for astronaut training at altitudes up to 120,800 ft (36,820 m).
After Yeager's Bell X-1 flights, Scott Crossfield sets a new record in the Douglas D-558-2 Skyrocket (represented in this film by a modified Hawker Hunter).
In the scene where Alan Shepard is introduced, we see him landing this on an aircraft carrier (the USS Coral Sea), in an A-4F masquerading as an earlier A4D-2.
On the USS Coral Sea, we see several A-7 Corsair IIs (inaccurate for this time period) probably masquerading as Vought F8U Crusaders, which they slightly resemble.
Grumman C-1 Trader
This retrieves Alan Shepard after he re-enters Earth's atmosphere in his capsule.
Three UH-1s are seen in the movie, a UH-1D painted as a NASA helicopter and 2 US Army UH-1Hs visible in the background during the same scene.