The date on milk is a sell-by date, not a use-by date (on all the milk I've ever bought, anyway), and is good for some time after that date. How long depends on the fat content of the milk (which is what spoils) -- skim milk will keep the longest, whole milk the shortest.

I have milk in my refrigerator right now that has a 1/5 date stamp on it. Just had a bowl of cereal and tea for breakfast this morning, and it all tasted fine.

You can trust me on this one -- I am an uber-paranoid freak about expiration dates!!