I've been trying to figure this out all day. I'm thinking it was probably Aliens, though I remember seeing The Fly around that time, too. Either my parents were crazy or realized the obvious - that I could handle it.
What shocks me is that while working at a movie rental store, with people who claimed to have watched a lot of movies and were around the same age as myself, that most of them had never seen these two movies.
Jungle Book, when I was 4, at the famous High Street Theatre, in West Chester, Pa. It's famous due to its cool Art Deco 1920's architecture. (I'd like to add that it was already ancient when I was there!