When I was a kid, we would turn over the bottom of the shoe box and cut out 3 mouse holes, one smaller than the other, and then try shooting marbles into the holes. It was a very enjoyable game. You got 25 points if you got it in the smallest hole.
My mother wasn't big on keeping shoes boxes, except maybe for a storage use for other stuff. I am not one to keep shoe boxes, either. Except if they're fancy shoes, and I don't have much of that.
Shoe boxes are great for storing old photographs in.