I really can't remember. I think my parents took us to the drive-in. I remember playing on the playground equipment at the bottom of the giant screen. But I don't remember the movie(s). The first movie I remember taking myself to was Star Wars (I think).
EDIT: Oh! I remember riding the bus into town early in the morning, along with the neighbors on Saturdays. We would go swimming at the YMCA and then grab a burger and fries at the Big Boy. We would then catch the matinee at one of the theaters. It was always a King Kong, or Godzilla type movie, sometimes it was a Tarzan movie. I was about 10 or 11.