How many days can raw egg whites can be kept refrigerated?

Eggs should ideally be eaten within a week of purchase but they are fairly durable. As time goes on the albumen (white) deteriorates but protects the yolk. The goodness (for the chick, at least) is all in the yolk. In a pack of refrigerated eggs that are a couple of months past their "best before" date, some of the eggs will probably be rotten (reddish tinge, watery, smelly) but in some, the whites will be almost like water but the yolks will still edible, although they certainly won't taste as good.

The albumen oxidises quickly inside the shell (which is air permeable), but outside the shell it's not advisable to keep the whites for more than a day or so. It shouldn't harm you if you do keep them longer, as long as you cook them before eating, but their useful properties will diminish quickly.