I have seen Titanic and Forrest Gump as well....and I am not sure how they are considered sad movies. My daughter "now 15" still goes around sometimes and says.....Jack, a boat.

And I remember in the theatres that I busted out laughing when the guy fell off and hit the propeller...DING....lol
Those two are actually both my candidates.
Titanic not because Leo died or anything whatsoever related with the romance or the dummies flying around to their death, but because of the scenes about the people who got locked inside and had to die, simply because they're considered 'lower class'. They were denied a chance to save their lives because they're poor. It's just brutal.
Forrest Gump because of the very first scenes with Forrest sitting on the porch while his mom had sex with the principal(?) so he would accept Forrest to his school. As I recall she made some 'funny' noises and people in the theater laughed (including my date at the time). I did not find this funny at all because of the context and was very disturbed watching that scene.
I watched these two movies exactly one time in my life. These two scenes bothered me so much I did not want to watch them anymore after the first time.
Anyway, I still haven't decided on the saddest movie I've ever seen. As you can see from above I got emotional very easily when watching a movie, so I got to think about it some more. There are are many other candidates out there
