Mushrooms

Photo © Flickr user stu_spivackStore fresh mushrooms in a paper bag inside of the refrigerator. Do not keep them in the crisper.
Nuts

Photo © flickr user macinateStore nuts in the shell until you are ready to use them. Refrigerate or freeze any that you plan to keep for more than three months.
Onions

Photo © Flickr user Darwin_BellStore whole onions in a cool, dark place away from moisture. For bulk storage, cut the legs off of a pair of pantyhose; drop an onion into one of the legs, and tie it off. Then, drop in another onion and tie it off again. Continue doing this until the legs are full. Then, hang
Note: Potatoes give off a gas that ripens onions, so be sure to store them separately.
Pineapples

Photo © Flickr user annaestasyeahStore whole pineapples unwrapped in the refrigerator. Store cut pineapples in the refrigerator in an air-tight container.
Potatoes

Photo © Flickr user clayirvingStore potatoes unwashed in a paper bag, pantyhose or a similarly vented container. Then, place in a cool, dark and dry spot.
Tomatoes

Photo © Flickr user jackideeStore tomatoes at room temperature. Keep out of the sun, once they have ripened.