Keeping the horse moving forward is obviously key. If the horse is moving forward, it cannot rear.
I have a CHRONIC rearer so I can tell you the things I have tried and the things that have... worked. Many people have a problem with the methods I've tried, but my horse is one that could not be sold because his rearing issues would have shortened his life-span tremendously (he would have hurt someone or ended up in an auction and spiraled down from there). And I want to say that I do now, and have always loved this horse. Even with his faults.
The first thing I did was ensure that my tack fit properly and he did not have any health issues. (Since his rearing started at three and continues now at 25, I think we can safely assume there is no pain issue)
I have used a tie down of sorts. I'm not really sure what it was really for, I'm assuming speed eventers. It was not a fix. It was a device that I could use to keep him from lifting way up. When he had it on, he did not rear as much, but he knew when he wasn't wearing it.
I was told by an old-timer once to tie a piece of bailing twine from his tail (the dock) to his halter so that when he reared he pulled against himself. I did not do this right, I tied it to the tail itself and only managed to yank a chunck of tail out.
I tried a water balloon and an egg once. The idea is to make them think they have hit their heads on something. I wasn't fast enough, because you have to hit them on the way up and NOT on the way down, so I just really made a big mess.
My brother made me a num-chuck looking thing out of an old broom handle to hang on the saddle horn. This worked the best, I've also been told to try a rubber hose. Basically on his way up, I popped him between the ears and he came back down. He'd rear maybe once or twice during the ride and decide not to do it anymore, but every day was the same.
I also figured out that if I yank his rein to the right or the left (hard) while he is in the air, it will knock him off balance and he will have to throw his front feet down to get his balance, once his feet hit the ground I can kick him forward into motion so he cannot rear.
I also learned that when I feel the bunching of the shoulder muscles I can jam my knuckle into his spine, just above the withers, that will keep his rear down to about 18 inches and much less dramatic.
I have been told to flip him over on his back in mid rear but I refuse to do that one. My horses life and my own is worth more to me then that. He's 25 and when I bought him I was only 15. MAYBE with a trainer I could have fixed his issues. Maybe not.
From this experience I have promised myself I would never own a horse that rears again. And I have also decided there is no cure for the rear... but that is my humble opinion.