Myself, I've only had maybe three hatchet cuts worth mentioning. Two were while sharpening. I've discovered (because of this) that it really repays the extra effort to set up for sharpening in such a way that your hand will be blocked (by, say, the edge of your workbench) from cutting itself on the blade. (For example, if you can keep your fingers on the side of the file opposite the side that's filing the blade, rather than wrapped around the file--or you can set the blade up so that, if you slip, your knuckles will hit the side of the tree stump or whatever that you're resting the blade on, before your fingers hit the blade.)
The other memorable cut I've had I got when I was trying to use one of the edge-exposed tomahawk carries shown in Dwight McLemore's great book The Fighting Tomahawk. It worked for a while, then, probably predictably, one of my hands swung to the wrong place, and I ended up with a very curiously-irregular zig-zagged cut--fortunately pretty superficial--on the heel of one of my palms. Took a few days to heal completely. Nowadays I always use some kind of sheath when I'm carrying a tomahawk for any significant period of time.
Seems to me that as a camp medic I've seen some worse axe cuts. The best, most-detailed edged-tool-safety instruction I have ever seen is in Mors Kochanski's book Bushcraft; I commend this to anyone interested in edged tool use in the outdoors. (Or anywhere else, actually.)