First movie I ever cried to was Saving Private Ryan, not at the end, though. I cried when Capt. Miller revealed what his job back home was. I was a lot younger then and war seemed a lot more glorious for me at that age (considering my war experiences were along the lines of Medal of Honor and Call of Duty), so when he tied the people in war to a life I can relate to it just brought home the fact that everyone who was fighting in that war was a human being who was there, not for glory, but because they had something they felt they had to protect. That fact had never really clicked in before then.
Now I've got a girlfriend so I tear up at just about anything sappy. =P
In my defense I've actually tried to make myself more emotional over the years. It's a heck of a lot more fun really getting into movies, games and books rather than just sitting back detached from them.