New grocery bag alternatives are popping up everywhere, but re-market is one of the first places I've seen re-usable produce bags. Bags are sold in various sizes, from large bags suited to your potato stash to small bags for more delicate fruits and berries. All bags allow the produce to breath and are transparent so that you can see what is inside. They are also quite a deal, with a mixed size set of 6 running around $15.
Image from remarket
Image from remarket