I have occasionally broken the skin while climbing, but mostly outdoors

I always have scrapes and grazes; currently they're on the backs of my knuckles and one elbow. Before that, I did on one occasion resort to taping my knee as a particular move was shredding it even through my climbing trousers.

However, I suspect this may be partly due to my clumsiness and partly to the route-setters' remarkable sadism and fondness for knee-bars.