Daniel is spot-on with his answer. I'll elaborate on it a bit here.
As indicated by his bottled water in the freezer trick, a full freezer is a happy freezer. The same applies to the refrigerator too. While I wouldn't put random bottles of water throughout my refrigerator, it's important to know that the fuller your refrigerator is, the more it holds its temperature when opening/closing, and the less energy you'll use. However, you don't want to jam pack it so full that there isn't any airflow around your stuff, because this can hamper the cooling efficiency as well.
The ideal refrigerator temperature is 35°F (1.6°C). You're not hugging the danger zone like you would be at 40°F (4.4°C), and you're distancing yourself sufficiently from 32°F (0°C) that you don't freeze half the stuff in your refrigerator. That said, the temperature within your fridge can vary rather significantly with normal usage.
The coldest parts of your refrigerator are the back, and the bottom. The back because the cooling element is there, and the bottom because warm air rises. If items you don't want frosty are getting frosty, then move them away from the back of the fridge. I would avoid putting items in the door of your fridge that are particularly sensitive to spoilage. The items in the door of your fridge can easily get as high as 59°F (15°C), and do so often. Putting milk and eggs in your door will significantly decrease their shelf life. Butter is OK in the little covered section in the door, because the door actually helps keep it's temperature a little better. You also generally don't want rock solid frozen butter.
So, put your meats on the bottom shelf in the back, your condiments (mayo, ketchup, mustard, etc.) in the door, and put everything else where it fits.
Just to clarify a couple of things that others have said -
The skin of any vegetable or fruit has natural defences against microorganisms, particularly moulds - if you wash your food the minute you get it home, you reduce its keeping qualities. Wash things as needed, immediately before using or eating them, and they will keep longer than if you wash them in bulk.
Never neglect the washing, because they may have been sprayed with something to improve their shelf life - and remember this includes things like the peel of citrus fruits, which is often ignored by the pros.
It is a fact that chilling foods can initiate mould growth, which will manifest itself quite quickly if the temperature is raised. If food was chilled when you bought it, keep it that way and the mould growth will be slowed down. If you put it in the chiller, keep it there until you use it.
If you bought food at room temperature and it quickly goes mouldy, you can usually bet that it was chilled in transit.
Best Answer
You generally do not want to refrigerate tomatoes; they will will get mealy in texture, which can be unpleasant.
Bananas are more complicated. Once you refrigerate them, ripening will stop, and it will not recommence when they are brought back to room temperature. So you never want to refrigerate unripe bananas.
Ripe bananas can be refrigerated to make them last a few days longer, but the skins may darken, which some people find unacceptable.