Never use other boarder's stuff without asking.
Don't use someone else's bedding (I had a problem with my bedding going missing, it's $10 a bag/I own two horses/we have large stalls - you do the math. I was beyond livid.)
If you turn it on, turn it off - if you open it, close it.
Don't give "snacks" to other people's horses, especially if that horse has a sign on the stall saying don't feed me.
If your horse is standing in the isle, and someone is trying to come through, even if there is plenty of space, just be polite and move your horse.
If there are studs on the property, and you need to turn the electric fence off for whatever reason, TURN IT BACK ON. My BO is a breeder and has two studs and a bunch of broodmares, we're a large barn but thankfully only a few boarders, and for some reason there's always somebody who unplugs the hotwire and fails to turn it back on. One of my mares will be bred, quite possibly to the BOs stud, but she's in the middle of her show career so I don't need an unnecessary breeding currently. My other mare's broodie days have been over for some time.
ALWAYS clean your horse's poop up.
ALWAYS sweep. One of my biggest pet peeves is people who don't sweep up at the very least in front of their stalls.
Unless you're at a barn that leaves jumps and things up, PLEASE clean them up after you use them. I was once at a barn that the boarder's rarely cleaned up their jumps, and when they did they had a massive pile of jumps in the middle of the indoor that was seriously annoying to ride around - it was a big mess basically.
Also with the jumps, depending on size of the arena, and if there are others riding, just do the polite thing and double check that they don't mind if you set up a few jumps (if you jump).