For rearing, you want to lean forward and give your reins slack. Horses won't go over on their own, and are normally pulled over by the rider. Once the horse comes down, MAKE them move forward immediately!
For bucking, try and wrap your legs around the barrel of the horse. Grab mane or the front of the saddle. If a horse starts bucking on me, I am normally not nice, and I will give the bit a chuck or two if I have to. Try and get the horses head up.
If you are coming off at a fence, you are more then likely making a mistake, like dropping the horse, no leg on, and jumping ahead. Posted via Mobile Device
If you're position is correct you'll fall off less often.
Obviously you can't do this 100% of the time ;). Also make sure you don't look down, look where you want to go. Which is probably not the ground. ;P
I try to ground myself a la Centered Riding by Sally Swift. I try to "blob" myself out so I fill up as much of the saddle as possible so I'm heavy like a sack of wet cement. I try to sit square and hope it's just one buck. Haven't been a horse that rears yet...hopefully never!
If I am about to fall off and know there is no hope for me to try and stay on the horse's neck is a beautiful thing to hold onto and slide off of =D I have only had one really bad fall and that was on my friend's horse but with my horse it's me not paying attention and end up coming off. I had Gidget rear up on me a month ago(found out the girth was hurting her cause she gained weight and needed a bigger one) and I just leaned forward and put weight in my stirrups and I stayed on.
I have fallen off that many times my body just does what it's suppose to do...LOL
Bucking you need to sit up and a little bit back and lift your reins to pull your horses head up. Then sit deep and ride the horse on his/her quarters so they are riding "up hill" <---have to do that with my young horse in showjumping lessons as he will "trip" and go while i'm down here I might start bucking, my instructor taught me how to prevent it.
BUT if it's happened and your on your way down, don't bother about the reins just grab for the neck and hope you land on your feet not your head....try fall off clean (unless your out in the middle of nowhere or cross country) I usually landed without reins.
Rearing, grab mane, follow your centre of gravitiy, so lean foward and give the reins to the horse, no point arguing now. If you know they're about the rear then one rein stop and disengange their quarters. My older horse ozzie that knows better would get all full of himself and you can feel the build up to it so I one rein stop and tell him off, then that is it for a long time LOL
Refusal of jumps......sorry got nothing. Wear a helmet and get lessons LOL most of my falls are from refusals so I got nothing. Turned my eventer into a dressage horse and my young horse is my up and coming eventer