The first movie hit theaters in '95, and I saw it on video after the fact, which means I was...four or five when I saw the first one, making me young enough to still believe that my toys might actually be a living thing (lol animism). The second one came out in '99, so I was about eight or nine, not much younger than Andy.
Now, Toy Story 3 came out in 2010, and hey lookie there, I'm 17, going on 18, preparing for college for the end of the school year, learning that I need to grow up and face the real world and wishing I'd had more time to enjoy my youth.
I was one year old in 95, so I definitely didn't understand the movie when it first came out.
I tried not to cry.
Though, it was probably effected by several factors:
1) I don't cry due to movies, especially children's movies.
2) It took them 11 years to come out with TS 3. By that time, I didn't really care that 3 had come out and only watched it because it happened to be on one of the DirecTV channels.