It's extremely difficult to find a great movie that doesn't have a single funny moment in it. Most non-comedies find room for some comic relief, and if the movie is otherwise great then the comic relief doesn't usually fail.
The Shawshank Redemption comes very close to being elite while being totally unfunny, but I enjoy the line where Red bemoans the fact that he doesn't have Rita Hayworth stuffed down the front of his pants right at the moment.