Absolutely. Many half blind horses are just fine for riding, and are just as reliable as any horse. We had a mare who severely scratched her cornea before we got her which caused her to go blind in one eye, and she made a very safe, very reliable lesson and ranch horse for us until we had to put her down of old age. I did find that sometimes she would get a bit 'sticky' on her right side and not want to soften up as easily when turning that way- but it only took a bit of work and confidence boosting to get her turning beautifully again. We plan to saddle train our 11 month old colt with only one eye once he's matured as well, and will not limit him.
As for jumping, I'm not sure. Perhaps small classes under 3', if you worked hard with them and were willing to be their eyes when turning blindly into things. The horse's depth perception might be a bit messed up so I'd ok it with a vet first and make sure to have a good trainer to help you.
Other than that I'd say just take it one step at a time!
I rode a lesson horse a number of years ago that only had one eye. He was a jumper, granted it was mostly lower level work. I'm not sure what level you'd like to get to and how severly one-eye blindness would limit a horse's abilities...but it can be done! He was one of the better lesson horses I rode and only having one eye never seemed to hinder his abilities. As previously stated, talk with a vet and have a great trainer behind you. If you train him slowly and don't overface him (if he doesn't already know how to jump) there should be no reason the blindness should limit him.
The horse I am riding know is partially blind in one eye. He was just broke. Took him on vacation and he was less spooky then some that have been ridden for years. My friend also rides one that is partially blind and he also does great. I can not answer about jumping tho. I would think if you took your time and learned to cue him he would do okay.
I have one who is practically fully blind but still has some slight sight in his right eye. I would not recommend jumping him. I would work solely on forming a great bond with this horse. Most horses who go blind and have a good trust for there rider/handler will be unstoppable for pleasure riding when they lose there sight. Some horses who are losing there sight tend to be a bit more spooky then blind horses.
The reason I would not jump him is because of his sight. With out having a full vision the horse could mis jump and get him and yourself hurt. I have however taught my horse to pick up his legs and a certain tap on his legs will guide him to how high he must step, but we are not trotting or cantering we are simply walking over it. It took time and I had to work on this before he went blind and am still working on it.
If you want to compete in jumping I would not buy a blind or part blind horse.