Not gonna lie, this gets me too.
I tend to not cry that much at films, but I sometimes flip into massive sentimental mode. The Fountain does that to me.
The films that really make me cry, like Life Is Beautiful, I hardly ever watch, because... they make me cry :(
Also, despite saying I don't cry much, Apollo 13 puts a tear in my eye. It feels like a pitch-perfect heartstrings puller. You know what's going to happen, you KNOW you are being manipulated like fuck, but hell, when them parachutes appear...