According to Patricia Michelson, who owns one of the great cheese shops in London, this is how to store cheese best:
Hard cut cheese (i.e. cheddar) should have plastic wrap on their cut side and the crust should be left to breathe naturally. As most of us don't buy cheddars with the crust still on, I'd take that to mean wrap the whole thing. She believes the plastic wrap should be replaced each time the cheese is unwrapped.
For bloomy crust (i.e. brie) it should be wrapped in foil or waxed paper.
For blue cheeses, wrap in waxed paper then foil.
Goat's cheese should be put on a plate with a food bag loosely covering it, or in a tupperware container with a tight lid.
What she does not make clear is whether cheese should always be stored in the fridge. Cheese has been around a helluva lot longer than refrigerators have. Some purists use cheese-keepers for their cheese. But these purists also tend to buy small amounts of cheese on a very frequent basis. So they aren't keeping huge blocks of cheddar or whatever...
Anyway, here's an interesting article:
http://lifeandhealth.guardian.co.uk/food/story/0,,2271870,00.html