Came across this list and thought I'd share...
Apples
Store apples in the fridge so they don’t get mealy. Keep other produce away from this high-ethylene-producing fruit to protect them from premature decay, or store your apples in a sealed bag.
Berries
Blackberries, blueberries, raspberries and strawberries should be refrigerated in a sealed container with a little airflow and lined with towels to prevent the buildup of moisture. Keep the lid slightly ajar or use a container with holes in it.
Broccoli
Since broccoli is a winter vegetable, it can handle cold temperatures. Keep whole heads of broccoli in the cool crisper drawer and wrap them in a damp towel to stay fresh.
Carrots
Submerge cut carrots in a jar of water. They should last for two weeks.
Whole carrots can last in the fridge on their own for a while.
Citrus fruits
Generally, it’s best to keep grapefruits, lemons, limes, oranges, tangerines and other citrus fruits at room temperature until they hit peak ripeness for a week or so. After this, put them in the fridge.
Corn
Keep corn from drying out. Store the ears still in their husks in a reusable silicone bag and leave them in the crisper drawer until you’re ready to use them.
Cucumbers
The flavor of cucumbers is impacted by cold temperatures so store them on the counter. To extend their life by refrigerating, wrap them in a towel so they stay dry and store them in a reusable, cloth grocery bag for ventilation.
Herbs
For soft-stemmed herbs like basil, cilantro, dill, mint, parsley and tarragon, place the stems in a jar with a few inches of water and put them in the fridge.
Hard-stemmed herbs like chives, oregano, rosemary, sage and thyme should be wrapped in a damp towel and stored in a sealed container in the crisper drawer.
Onions and garlic
Onions and garlic can be stored together, but keep them away from moisture in a low-humidity environment. Both like good air circulation, so use a basket or mesh or paper bag.
Onions prefer a cool, dark place, like a closet or basement storage room and they will last for months. Once cut, refrigerate onions in a beeswax wrap.
Garlic can be left on a kitchen counter in a breathable container. Refrigerating garlic can make it lose some of its flavor.
Potatoes and sweet potatoes
Potatoes should be stored similarly to onions, but you should keep them away from each other. The gases emitted by onions will cause sprouting in the potatoes.
Keep potatoes and yams in a dark, cool place, like a root cellar, cabinet, closet, or drawer. Store potatoes in a basket or other open container to prevent spoilage.
Salad greens
Wrap salad greens in a light, reusable dish towel to soak up water and keep leaves from getting soggy.
To revive limp greens, submerge them in a bowl of very cold water before eating.
Summer squash
Summer squashes like zucchini are similar to cucumbers, but they need to be refrigerated. Don’t chill the vegetables at temperatures any lower than 50 F, which might cause chilling injuries.
Tomatoes
Keep tomatoes out of the refrigerator. Store fresh tomatoes upside down in an open, flat container at room temperature and out of direct sunlight.
If they’re very ripe, refrigerate them until ready to use. Tomatoes give off ethylene gas, so keep them away from other fruits and vegetables.