Time.com has an interesting (though short) article asking why animated films--still, unfortunately, assumed to be for kids--so often make adults curl up into the fetal position and let loose. The author mentions a few specific tear-jerkers, which make sense: Dumbo, The Lion King, The Fox and The Hound, Bambi, and Wall*E. Actually, The Fox and The Hound was the first movie to make me cry.
However, the focus of the article is mostly on Toy Story 3, which made tons and tons of people--including myself--sob in their seats. The author was apparently crying when the toys are about to be incinerated. Knowing that Pixar would never kill off its characters like that, I wasn't sad at that point; I was simply stuck in the intensity. The waterworks scene is at the end, when **SPOILER (if for some insane reason you haven't seen the movie yet)** Andy gives the toys to Bonnie and the two of them play together. You're saying goodbye to Andy's childhood, and, in a way, because animated characters are so easy to project ourselves onto, we're reliving the times when we had to say goodbye to our own. We all remember that moment or series of moments when we became 'grown-ups'. For all that we've gained, there's that sense of innocence and wonder that we know is gone. That's why we cry. It's not because we think Woody is going to melt.
For the other movies, we cry for different reasons: Dumbo is separated from his mother, Simba watches his father die and thinks it's his fault, Bambi loses his mother and doesn't understand, Todd and Copper can't be friends anymore because the world says so, and Wall*E forgets who EVE is because he sacrifices himself to save humankind. These are human emotions for intense moments and crises in life--love, death, and separation. How can we not cry?
h/t Pixar Blog