Forrest Gump met President Johnson to receive the Medal of Honor. He met President Nixon to receive an award for player of the year while on the national table tennis team.
He won the Academy Award for Best Supporting Actor for From Here to Eternity (1953).
The best movie award to win is the Academy Award for Best Picture.
nuthing........... or at least in 2011
Yes the 2007 version won some award, link is below.