At the local supermarket they markdown packaged meats starting a day before the listed "sell by" date. It averages anywhere from 1 to 3 dollars off the price. With certain cuts of meat, this can be a nice savings for the pocketbook - especially if the item was already on sale that week!
The trick is to immediately prepare or freeze the meat. If the latter, when you thaw it do so with the expectation of cooking it that same day.