I always wear a vest when jumping and I require my students to also. They are designed to help prevent internal injures as well as to protect your back.
I had a student that wasn't ready to jump anything higher then a little X. Her balance and riding skill just where not up to jumping higher. Her mom wanted her jumping and was trying to push me to let her jump higher, I refused and they moved to another barn. The first lesson she took at the other barn she was told she wasn't to wear her vest (and her mom didn't push the issue). She was riding for maybe 20 min before he had her canter a 2'6 jump. She came flying off, landed really hard and couldn't get up. The instructor told her she was fine and helped her up and wanted her to get back on. She told her mom that something was wrong and they went to the hospital right away. Turns out she split her liver, if she had been a little later getting to the hospital she would have died. The vest would have helped prevent the injury from happening to that extent. She had a top of the line vest that fit her really well. She is now not able to ride at all, every, for the rest of her life because if she comes off again she will most likely be killed.
So, I will always promote jumping vests :)