What temperatures should I keep my refrigerator and freezer set at?

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.

Normally a domestic freezer is best set to ?18 °C (0 °F) or colder, as that's what the expiration dates for many food items are based on. It's also a requirement for freezers in restaurants, supermarkets & other places that sell food (at least here in Europe) to maintain a temperature of at most -18 °C.

A general purpose domestic fridge should be at around 1-4 °C (so, just above the freezing point, and below 5 °C). Normally it's not possible to set a fridge to 0 °C (at least not over here), but sometimes the temperature sensor doesn't work as intended, especially if there is a freezer compartment that is heavily frosted.

http://en.wikipedia.org/wiki/Refrigerator has some more info, and also lists some alternative temperatures for special purpose fridges & freezers, e.g. for fresh fruit a normal fridge is too cold.

Some refrigerators are now divided into four zones to store different types of food:

• ?18 °C / ?0.4 °F (freezer)
• 0 °C / 32 °F (meats)
• 5 °C / 41 °F (refrigerator)
• 10 °C / 50 °F (vegetables)

In order to keep food out of the Danger Zone, your fridge must be set between 32-40°F (0-4°C). Your freezer must be below 32°F (0°C). I keep mine as cold as it will go. Keep your freezer efficient by half-filling it with bottles of water.

(I'm not sure if this question will stand, as it is broadly off-topic. But there is a specific and expert answer, so...)

I've always been told to keep freezer at 0 F, with fridge no higher than 40 F. Alton Brown recommended buying a pair of those hanging temperature gauges (one for each compartment).

If you keep potatoes in the fridge they should not be stored at temperatures below 7 °C (45 °F). If, that is, you intend to use them for roasting for frying. At lower temperatures the starch in the potato breaks down giving a burnt look and a bitter taste after roasting.

My fridge, which stands about six foot, appears to have almost 4 °C of difference between the temperatures at the top and at the bottom. This means I could have potatoes at the top and items that spoil more easily lower down. At least I could do that if the piece of junk would maintain a consistent temperature.