1961 - I'd say West Side Story, but the score wasn't written for the film. So I'll go with El Cid.
But my favorite movie of that year is One, Two, Three, and my current avatar is my first record - Khachaturian's Sabre Dance - which was the basis of the score. So maybe I should go with that!
It was none other than Hugo Friedhofer's "One Eyed Jacks", which was also the very first film score I ever heard (I saw the feature film two years later).