If you're planning on cooking with peaches (like I did with the peach puzzle), you'll want to peel them first. Cooking causes the skin to become rough and the texture could be unappetizing in pies, etc. However peeling peaches seems like an messy task. 
The worst part of peeling vegetables is the clean up. I used to peel them over the sink and then scoop everything up afterwards. It was a slimy sensation that I decided I could live without. 
