The real label you want to look out for is "Use By," which provides the best clue for freshness. Once that date passes, the food won't be at its best quality.
Date labeling is only required in about 20 states (it's mandatory in all 50 for infant formula), so sometimes your nose and eyes are the only tools you have to rely on. But if you store things properly, you can extend the life of most groceries by weeks after purchase—or indefinitely, if you freeze it.
Here's a guide to how long some common foods stay fresh when stored in the fridge (at 40 degrees Fahrenheit):