Refrigerate all other fruits and vegetables not listed above. Almost all fruits and veggies should be wrapped in plastic and kept in the crisper drawers.
Store soft herbs such as parsley, basil, dill and cilantrolike flowers -- put them stem sides down in a glass filled with water and put a plastic bag loosely over the top. Store woody herbs such as rosemary and thyme in plastic bags, loosely wrapped with paper towels.
Wrap harder, drier cheeses such as parmesan in foil or wax paper. Store softer, wetter cheeses such as brie or mozzarella in plastic and change the plastic wrap often.
Overripe bananas freeze beautifully in their skins and frozen grapes are delicious. Rinse and dry the grapes well, then freeze them individually. Once they are frozen transfer them to a resealable plastic bag and squeeze out the air. Freeze berries the same way.
Sara Moulton also recommends these books about keeping foods fresh:
"One Dish Dinners," by Jean Anderson
"How to Pick a Peach," by Russ Parsons