Refrigerate:
Keep them in separate bags and use them within three days for best freshness. However, many can be used past the three days. I've kept some for weeks. The flavor and nutritional value will just deteriorate over time. Store your fruits away from your veggies so that the ethylene produced wont adversely effect your vegetables.

FRUIT

• Apples (past 7 days)
• Apricots
• Asian Pears
• Berries
• Cherries
• Cut Fruit
• Figs
• Grapes
• Rhubarb (wrapped in plastic)

VEGETABLES

• Artichokes
• Asparagus (with a moist paper towel around it)
• Green Beans
• Beets
• Belgian Endive
• Broccoli
• Brussels Sprouts
• Cabbage
• Carrots
• Cauliflower
• Celery
• Cut Vegetables
• Green Onions
• Herbs (not basil) (Wash and dry before placing in the fridge. Store with a paper towel. Or, place in a jar of water, like a vase, covered with a damp paper towel.)
• Leafy Vegetables
• Leeks
• Lettuce (after washed, store in bag with paper towel to absorb moisture)
• Mushrooms
• Peas

Wait to Refrigerate:

• Avocado
• Kiwis
• Nectarines
• Mangoes*
• Peaches*
• Pears*
• Plums*

*until they are slightly squishy

Don't Refrigerate:
Some foods won't ripen when refrigerated. They won't be allowed to intensify their flavor and texture. Some will even taste bad (tomatoes for instance). Have I refrigerated some of these before? Yes. Did I die? No, but this will just help you get the best flavor.

FRUIT

• Apples (fewer than 7 days)
• Bananas (bananas actually can be refrigerated, the peel will go brown but the inside is fine. I do this when I have bananas that are about to go overripe.)
• Citrus fruits (lemons and limes absorb flavors from fridge)
• Mangoes
• Melons
• Papayas
• Persimmons
• Pineapple (store upside down to allow sweetness to run throughout the fruit. Sugars store on the bottom.)
• Plantain
• Pomegranates

VEGETABLES

• Basil (in water)
• Cucumber (can be refrigerated if used soon after pulling from refrigerator)
• Eggplant (same as cucumber)
• Garlic (keep vented)
• Ginger
• Jicama
• Onions (keep vented)
• Peppers (same as cucumber)
• Potatoes (keep vented and cool, if refrigerated before cooking, starch will turn to sugars and go sweet.)
• Pumpkins
• Sweet Potatoes (keep vented and cool, keep only a week)
• Pears
• Plums
• Plumcots

Just so you know, most fruits and veggies can be refrigerated. Some herbs and lettuce can't, and melons don't do so well either, but most can.

Tip: Apples will enhance the ripening process. I would keep away from bananas, but if you want something ripened, go ahead and use one.