U-2 (1960)

The United States had been sending the secret U-2 high-flying spy plane over the Soviet Union to take pictures and gather information, when one was shot down by a Russian missile. The pilot Gary Francis Powers was taken prisoner and later released in an exchange for a Soviet spy who had been arrested in the U.S.
An interesting note is that Kennedy assassin Lee Harvey Oswald was stationed at the military base where Powers' U-2 took off for the flight. No connection was ever made, but it did seem suspicious,