At a sleep-away camp I once went to, the barn manager yelled at me for sitting down and saying I was bored. She said "You're in a fifty horse barn! You can find SOMETHING to do!"
My current barn only has 14 horses, but you can always find something. Refill and clean water buckets, cleaning tack, sweeping aisles... I LOVE doing carrot stretches in my spare time. Good for the horse and fun for them too! Sometimes if there is absolutely nothing (easy to do everything for 14 horses) I'll groom my horse really good, give her a bath, take her for a walk, or just let her graze.
I tend to look creepy at the barn if i'm bored...I don't work there so I wander and look for something to do...o.O but in the end I'll sweep, organize, write in a day planner or clean tack. I'll also take pictures, check the fitting of my saddle, or read ( if I have a book handy)
Play with my horse, of course. When I have energy to burn I usually run around the pasture and then run at him full speed... He hardly bats an eyelash, must be used to it by now and just thinks I'm a psycho. ;) Occasionally he'll follow at a trot... Since I'm not an incredibly fast runner.
And theres always little training things to do... Or walks to take. Or, as you said, cleaning.