I remember watching The Sting at a very young age. I remember loving Redford and Newman's repartee, and I remember not being able to follow the plot AT ALL. Then Sneakers came out when I was ten, and my dad took my brother and me to see it in the theater.
But even beyond the actual movies I had seen him in, I was always aware of his legacy, or at least his cultural impact. He was a Movie Star. In some ways he was the archetypal movie star, in a line you could trace from Clark Gable to Cary Grant to James Dean to him. I don't know that the typical child of today has that relationship with the concept of the movie star anymore.
I'm not trying to say that's inherently a good or bad thing -- I'm not telling the kids to get off my lawn quite yet -- I just find it interesting to think about. The media landscape between when we were kids and now has changed by orders of magnitude.