Which fruits and vegetables should be kept in a fridge, and which outside?
Apples, pears, and many other fruits are kept in cold storage after harvest, and keeping them in the fridge after buying them will help them keep longer.  Pears, peaches, and other fruits that are sold on the green side, should be removed from cold storage a day or two before using, to allow them to ripen a bit more.  Berries should be unwashed and refrigerated, and only washed right before using them.

Only a few fruits and vegetables are hurt by being refrigerated.  Bananas will turn brown, and tomatoes lose flavor.  

Some veggies, such as winter squashes, have a long shelf life outside of the fridge, and refrigeration does not really add to that.