Depends on the misbehavior. I knew a horse that would back up when he didn't want to do something, so to counteract that we had the rider back her horse up until the rider thought he was done acting up whenever he wanted to back up. Thus making his favorite escape, his least favorite thing in the world because it meant he had to work.
If the horse rushes a corner or gate in an arena you make them work the most in that corner to get them believing that the gate or corner means work and they stop rushing that area.
Normally I'd turn them in a circle because it forces their feet to move. When my horse misbehaved in the line-up at shows by popping little rears and refusing to stand still I started to turn her back towards the gate and had her face the opposite direction of the other horses, she stopped acting up in the line-up because she couldn't see the gate or the other horses move off towards the gate. Now she stands like a perfect angel in the line-up when she faces the correct direction, even as the other horses move off. She's knows better than to move until she's told to. This was a case where circling her wasn't working. The best counteractive measure is completely based on the circumstance.
Well at this practice we have, he was worrying about the horses and neighing. So I backed him up and he finally listened and was less worried. It wasn't that big of a deal but it just annoys me. I was just wondering what other people do
For consistent neighing, I haven't had to deal much with that, but if I don't want them to talk I usually say, "Hey!" really loudly and suddenly. Sometimes, only in extreme cases though where my voice won't get their attention after repeated tries, I give them a quick slap on the shoulder, only once though. I only use that as a complete last resort. Maybe try to face him away from the other horses and walk him forward? But if backing him up works, keep using it. Don't fix or change it if it isn't broken.
Like Tempest said, it greatly depends on the horse and the situation. Some horses, I will push them into little tiny circles, others I will back them up, and others I will just make them stop and stand until they regain control of themselves.
Some of the horses I just sent home are the type to flip over on you if you pushed them backward when they were freaked.
For the neighing thing, I usually just refocus the horse's attention. I'll start working them in medium sized circles, work on lateral flexion, leg yeilds, turnarounds, then let them stop and stand when they're relaxed, responsive, and attentive. If they start neighing again, then they go back to work.
I make them work. My horse likes to back and spin in circles when he is being bossy or doesn't want to do something. We spent the whole day backing and turning because, well...That's what he wanted to do. So we backed around the arena, turned in every corner twice. Now he stops when frustrated or something. I have that problem being fixed too, :)
I have never been one to back one up to punish a horse. I don't even really do it for one that fell through his stop or is thinking too forward. I found using backing usually creates more issues, the extreme being rearing or flipping over backwards.
I usually trot small circles and depending on the level of training and what I may be getting after him for, a counter bend trotting a small circle, then roll back in the direction of the counter bend, two-tracking, and so on. Then make the original work or idea the easy thing. I try not to do the same thing every time or change up the order or some get wise and will "punish themselves" before you have a chance to. I have seen this with the backing and those who spin a horse as punishment and make a BIG deal out of it rather than staying calm and just re-directing and using the energy into exercises that are a little harder and requires attention.
Leg yields and deeeeep corners and deeeep small circles. For the kind of horse that just isn't going to be dandy doing what we want for that session, you know the kind, the kind that's bored out of his mind and in a stall 90% of the day, I jazz up a varied routine of new, engaging things for him before asking him to do whatever I wanted... There's a little TB next door that when she gets frisky, is directed to a ready small jump and is calmed after popping over it. High spirits = energy, so use it ;) Usually when the horses I ride get nutty, they're anticipating and wanting to rush, so I do a bunch of various speeds and serpentines.