Typically either drowning, or getting conked on the head by the boom, though obviously puncture wounds and/or deep lacerations, as well as burns, are always possible.
I've been hit hard in the head with the boom, during a sailboat race no less, which was no damned fun, but thankfully I was not concussed, which was a bit of a miracle in itself. It did, however, end the race for us, which I argued against at the time, as we were beating one of our regular competitors boat for boat.
We did have a larger more complete medical kit that stayed on the boat, which included a flaregun, emergency blankets and rations, splints and gear for more extensive wounds. Thankfully, aside from using the emergency blankets on one cold, becalmed night, we were never called to use either kit.
The kit I referred to above went with me everywhere in my purse.