New Balance has a few of their lines with a Gore-Tex liner. I’m not sure how well it’d stand up to heavy downpours, since you’d be getting water coming in where your foot goes in to the shoe, but puddle and such, they’re champs. I wore them walking through a grassy field that was wet from a recent downpour and my socks and feet stayed perfectly dry.

I find it near impossible to start a run when it’s already raining, however, if it starts raining while I’m running, I love it. My favorite runs have been during absolutely torrential downpours. It just feels primal.