E.T. I was three years old. All I remember is that the scene where the government comes to get him, and they're all wearing hazmat suits, scared the $#!% out of me. My mom had to take me out of the theater and we walked around the lobby until the movie was done. My brother is two years older than me, and he was pretty much left alone in the theater and he loved it.
My second movie was a year later when Return of the Jedi came out. I remember the line wrapped around the building. My mom took my brother and me to get ice cream while my dad waited in line. At one point, our spot in line was right by the emergency exit to the theater, and we could hear Darth Vaders voice through the door. When you're four years old, that's very exciting stuff. I am pretty sure I had not even seen Star Wars or Empire, but in the 80s, it didn't really matter. You still knew everything about the Star Wars universe.
I feel like those are two pretty solid films to start my movie going career on.
Edit: The following summer, Indiana Jones and the Temple of Doom came out. I begged to go see it, but my mom had heard it was really violent, so she wouldn't let me go. Instead, she rented Raiders on Betamax. I remember being upset because I wanted to see "Indiana Jones" not "Raiders of the Lost Ark." I didn't realize they were the same thing. I guess my mom was cool with faces melting off, but not cool with having your heart ripped out. It was one of only two times my parents decided to care what I watched. The other was T2. Generally, my parents took no interest in what I watched. I went to see one of the "Nightmare on Elm Street" movies (I don't remember which one) when I was in third grade. I had seen the entire "Friday the 13th" series by the time I was done with Elementary. They never cared. But for some reason, they took a hard stance against Temple of Doom and T2.