only occasionally when bottling or handling yeast. When I brew the only thing I touch that comes in contact with the cooled wort is the end of the racking hose. For that I think dipping my hands into sanitzer is just fine.
I have a full HazMat suit that I wear once the wort gets to below 120F.
Seriously, no. I've never worn gloves during any part of brewing and I doubt that I ever will. I sanitize my hands and everything else that I use very thoroughly (sometimes multiple times) every stop of the way so I've never seen gloves or some other type of protective wear necessary.