These are some thoughts that stem from my experiences and imagination. I've actually done some of the things that I suggest here, and I've only dreamed about doing the others, but I've included all of these ideas in an effort to convince you of the fun that you can have with a sling.
Reenactment: The SCA (Society for Creative Anachronism) is an excellent reenactment society, and members can use the sling for melee if soft objects are thrown. I suggest tennis or racquet balls. Likewise, Roman and Greek players could use the sling. They would make excellent functioning props.
Hunting: It's documented that slings can kill game. Along that same line, many hunters need to scare game out of dense brush. The sling is an ideal tool for accomplishing this. A stone ripping through the trees and underbrush makes a huge ruccous.
Survival: Slings have an advantage over conventional weapons in that they are extremely portable. You can carry it easily in your pocket. It would be ideal for hiking and camping since it is very light.
Merit Badge: A merit badge could possibly be produced from the effort and skill required to assemble a sling. Ideas for this type of project could be garnered by referring to the basic sling that I offer.
Games: (1)People stand at opposite ends of a field and toss racquet balls at each other. Great for honing your skills. (2)Launch a boat or floating object out into a stream and try to sink it. (3)Just see who can throw the farthest or most accurately.
Paintball: Paintball is one of the funnest sports around. Imagine lobbing one of those paint grenades a hundred yards away at an enemy bunker. :)
Personally, I just like heaving rocks out into the middle of still lakes and streams-- to see the splash of course. But, hey, do whatever you want. I carry mine hiking, walking, and lots of other places. You never know when you'll have some free time and a..... rock.