The Patriot: when his daughter finally speaks to him and runs to him and says "Don't Go! I'll say anything just don't go!"
This one gets me as well, especially since my wife and I started having kids (just had our second this past Sunday).
I saw The Patriot a few weeks after graduating from Basic Training. I got teary-eyed when Mel Gibson rode his horse into the final battle while carrying the US flag Gabriel had been sewing. The pride, and everything I had just gone through, all boiled up.