I give myself minor cuts while sharpening all the time - on par with a papercut, really, but super annoying when they fill up with the various oils, solvents, grits etc. that build up during an extended axe shaping/sharpening session.
My worst sharpening luck seems to be with draw knives. Not sure why, but they seem to nick me every time.
The only time I have ever had a cut requiring medical attenention was when I dropped a competition axe while I was greasing it for a competition. Bounced off a bone in my right hand - 5 stitches, just missed the tendon. I have also nipped my shoes a couple of times when training in the snow.
I always wear my chainmail when I practice. Always.