Luckily I have never had a bad episode with a broadhead, but I have sliced my thumb and my hand open before pulling them out of a styrofoam target. It's force of habit to put my left hand against the target face and pull the arrow out with my right. Just be sure your hand isn't too close to the entry hole where the broadhead went it. Especially with broadheads that cut both ways and are sharpened on the back side of the blade as well as the front.

Only once. I pulled a magnus stinger out of my target and bumped my shin with the backside of the broadhead. Bled like a stuck hog and left a nice beauty mark.

Ha good thread guys - About a month ago, while out on the 3d course I killed an unsuspecting sapling, of-course the rest of the fellows in my group started ribbing me. While I was freeing said arrow. Luckily for me I had left my 'super' sharp K-bar back in camp and only had a small folder on me. Hence I borrowed a blunt as a spoon quiver-knife from one of the guys! Inattention due to being distracted by above mentioned ribbing caused me to slice my thumb to the bone!! I still shudder when I think - if I had been using a sharp knife....
stay safe out there - pay attention and don't be complacent!! (oh and carry a roll of duct tape)

Back in the 60's, my hunting bud managed to bury a Razorhead in his thigh while negotiating a downed tree in his path.  Direct pressure slowed the arterial bleed, but it was a near thing.  The docs sewed him up, but watched him for a while to see if he needed transfusions.  Recovered ok, but as far as I know, he never bowhunted again.