No serious injuries with axes or hatchets. I came very close to a serious injury with a chain saw, back in 1982, helping friends on the Texas coast clean up after a hurricane. The moving blade came within an inch of my head while I was up in a tree. I looked down at the ground crew, and they looked up at me with horrified expressions. For effect, I screamed and we all laughed. But it was a lesson I never forgot--never have an important body part under the weight of a chain saw.
Now in my 60's, I have a good imagination about injuries informed by terrible examples of same I have seen, and for that reason I treat axes in use with tremendous respect and attention. In my history, only motorcycle and overturned tractor accidents were more terrifying (fortunately, none involving me--but for that reason I'm not a motorcycle person at all). It's a reason I tend to use longer axes even while shorter handles are becoming more popular. And it's a reason I always look (as with that chain saw) at the direction of momentum, and make sure that is away from any of me. Not using them when tired and befuddled also helps, just as with woodworking tools (particularly power tools).
My friends think I'm careless with knives, but I think it just seems so. One reason I like my Kershaw Leek as an every-day carry is that the opening assist means there is some resistance to closing the blade. When I'm closing a blade one-handed, my thumb is across the path of the blade when releasing the liner lock, and the spring assist helps keep the blade from just flopping around and hitting my thumb.
My biggest issue recently has been while sharpening and messing with sheaths. I've had to up my game with sheath handling after cutting myself a couple of times dealing with axe sheaths. And I now wear chain-mail gloves when sharpening. Leather probably would have been good enough, but I'm subject to bifocal mistakes these days--if it's not in the lens I'm using at the moment, the extra correction of a different lens displaces the object relative to reality, and I run into things accidentally. I have to specifically look at whatever it is I need to avoid in order to see it where it actually is. Unfortunately, I'm not always aware of what I need to avoid. Hence the chain-mail gloves when sharpening. In the field, I just keep the axe head at the other end of the handle, and moving away from me.
Rick "whose skin isn't as tough as it used to be, either" Denney