Tom Hanks in The Green Mile.
He was absolutely amazing to watch. Shooting the big finale scene required numerous stops and restarts. Every time the director stopped the scene, Tom Hanks would close his eyes and lower his head. He did not break character no matter how long it took to start shooting again and there were many breaks that went for 20 minutes or more. The rest of the cast and crew would mingle about or get a snack but he never moved from his mark until they started shooting again. Then he would lift his head and still be in character. And this scene took an entire day to film. Sheer brilliance.