Like Kevin, I would no longer mess with them. Good horses are too cheap and they are not worth it. But, I have re-trained several rearers and flippers that never reared again. Some of these horses I knew for years after I re-trained them and they did not rear again.
I am afraid I am going to have to disagree with just about everything that everybody said about rearing and how to 'fix' it. And, like everyone else, I do not usually give advice on how to 'fix' it. This is because if a person has the feel and timing to follow the directions on how to stop it , they would not have the problem to start with. Rearing is 99.9% rider error that lets it get started. Once the horse has learned that it can choose to 'stall out' and/or turn around and go home, it will continue to do it as a learned behavior. Then, it no longer needs a reason. It just does it because it has a learned habit to do it. Once it has learned this habit, it will fight tooth and nail to be able to keep doing it. Trying to stop it will usually only escalate it.
When I started out training horses for the public back in 1959, I was convinced that I could 'teach' a horse everything it needed to learn without using force or pain. I was convinced that if you built each training session on a series of steps and did not scare or hurt a horse, it would learn each new step without a problem. This plan worked. It was years before 'teaching' a horse became big business for clinicians that gave it a name. I was doing it 15 or 20 years earlier.
Then, people started bringing me their already spoiled horses. Quite a few of these spoiled dinks reared and several were 'flippers' -- horses that reared and fell over or threw themselves over on purpose. I was frequently the last stop for these horses before they were shipped to the killer plant. [Now, I would just let them go there.]
About that same time, a trainer I knew in Western Colorado was killed when a horse flipped on him and the saddle-horn put a rib through his Aorta Artery. I found, by trial and error, that my method of teaching was much less successful for horses with established bad habits. I could use things like 'taking a horse's head away from it', disengaging a horse's hind end, forcefully riding the horse forward, making a horse move it feet, etc and it is quite easy to get most horses to go forward for a trainer like myself. Trainers 'ride with authority' and many horses will not even try to rear with a trainer. Put a weak rider on that same horse and they will not go 100 feet without trying to stop or turn around and will immediately rear if that weak rider tries to get the horse to go forward.
The problem with what I call 'riding a horse through a problem' is that the horse will keep trying to stall out, especially with less assertive riders. The problem only gets 'sort-of fixed' for that day with that rider but the horse WILL try it again, particularly with a less experienced rider. If the object was to get the horse to totally 'give up' the behavior, continually riding a horse through the bad behavior will not eventually make a horse give it up completely. It just won't. It will just keep coming back with a weak rider or when asked to do something that it really does not want to do.
I tried various ways to get a horse to 'not want to rear'. It finally came down to negative reinforcement. You have to make a horse pay a higher price to repeat a behavior that he is willing to pay. It is really simple. If you punish a horse severely enough, it will give up the behavior and it will not come back. It is like an aggressive mean horse. You have to make a believer out of one. He has to know that you will hurt him worse than he can hurt you -- just as simple as that.
After the trainer got killed that I knew, I never got on another horse that I thought would rear. I had been lucky because I had had horses go over with me before. I had always been able to push away from them and stay out from under them. I had to find a safer way.
I started ground driving rearing horses. I found that they will do exactly the same thing while being ground driven as they do under saddle. They will stall out, refuse to go forward, start backing up, try to spin around, or just 'dummy up' and sull. They will do one or a combination of these things and will then rear if more pressure is put on them. I also found that I could punish one HARD for any of the above behaviors. I could get a 'feel' for what was going on in each horse's head as they stalled out and did whatever they did that came before they reared or flipped.
I found that I could take a 5 foot stock whip (or buggy whip) and I could spank the crap out of one. I could take the ends of a set of regular harness leather driving lines from one of my sets of harness. I could make one's life as miserable as I could until they gave it up. Most, would give it up, drop their head and just drive off like nothing had happened.
When a horse did drive on like a good horse, I would continue to drive it away from the barn and horses, drive it around out in a pasture for a while, drive it back to the barn and make it leave again. I would go back and forth to the barn for a couple of hours. I would make a horse drive forward, stop it and back it up and then make it go forward again. I put as much pressure on one as you could put from the ground. I wanted all of the resistance to show up and wanted a chance to 'fix' it in such a way that the horse did not want to repeat the behavior. I wanted to bring out the worst the horse had to offer so that I could combat it and fix it. Owners usually try to avoid the problems. As a trainer, I hunted them out.
Then, I would put my saddle on it and ride it roughly away from the barn again. The slightest 'hesitation' and I would take the ends of my harness leather reins and 'over and under' the horse and again make its life as miserable as I could. I wanted it to hesitate so I could put that much pressure on it to make sure it did not want any more of it. I found that like in so many other 'fights' with spoiled horses, when the horse gave up, it gave up. It would give a big 'sigh', drop its head, stop bracing and being stiff, frequently do the 'licking and chewing' thing, and all outward signs of resistance were gone.
Then, it was time to let other riders see if the horse had truly given up the ideathat rearing was worth the price it had just paid for rearing. I would put other riders on the horse and if it passed that test, I put the owner on it and gave the owner several lessons on their own horse. I would not take a spoiled horse in to re-train unless the owner agreed to take several lessons. These lesson were not your typical riding lessons but lessons in how horses think and the why and how of their horse getting spoiled in the first place.
In all of the years I trained these spoiled dinks for the public, very few went back to rearing. Many of these horses were horses I knew and followed for years. Many of them never offered to rear again. Some of them went on and made a name for themselves in the roping pen and barrel racing.
Re-training spoiled horses is sort of like making sausage or bologna. You would not enjoy watching the process, but it kept a lot of horses out of the kill pen. They did not have much to lose and I told their owners that.