I never cried when DiCaprio died. He was not a real person, and that always stood out in my mind. Strangely though, the part that always made me teary eyed is the part where the father puts his daughters into the lifeboat telling them to "hold mommy's hand and be good little girls." This was a comment similar to what 7 year old Eva Hart's father told her right before she left the ship.
It is also heartbreaking to see the Strausses laying on their bed, waiting to die, as well as seeing Titanic destroyed.