Gore-Tex in running shoes. The water will get in at the top of the shoe (as it is only 3cm high), and never get out, since Gore-Tex is watertight. Besides, when running, my feet sweat, so water will end up inside the shoe even if it isn't wet outside.
Actually, Gore-Tex has some fairly magical properties that make it both waterproof yet breathable (read as lets water out). According to their website ( http://www.gore-tex.com/remote/Satellite/toc/Tech