In my opinion, one of his greatest performances was 1998's Saving Private Ryan where he played Captain John Miller. When you consider war films in general with all of the angst and anger it is hard to have three dimensional characters. The role of Captain John Miller is complex and one I feel few actors have the ability to make real. Hank's makes the Captain all at once a superhero, a man who can't/won't loose and at the same time a confused and frightened human being. In the scene where Miller finally tells his platoon what he did back in the States, Hanks makes you feel like you are not in a theater anymore but actually on the battlefield with these soldiers sharing this experience. Frankly Lawrence Olivier never did that for me.
I guess the big question is when we find out what Tom Hanks can't do. He has managed to be believable as a captain in World War II, a sappy romantic lead or a mob hit man. You never know what you'll get out of Tom Hanks except for a great performance.