I'm not a big fan of eating stuff after any date on the packaging because it never tastes as good as it did before. HOWEVER, if it's a best by date, most of it can still be safely eaten. It might just be a little stale or have lost some flavor. My son won't eat anything after any date on the packaging.
So here are some foods that are probably still good after the best by date.
Milk - If it smells ok, it's probably good. Milk is pretty obviously good or bad.
Eggs - Usually still good weeks after the best by date. I've never had any problems with eggs. You can try the float test - if it floats it's usually bad
Salad Mix - If it looks ok it's probably still good
Dry ingredients - Flour, sugar, salt - all of these things can last for years
Canned food - Probably still good a couple of years after the date. Although I've noticed that it seems to lose flavor.
Find more foods still good past the best by date here.
Photo credit: SAUL LOEB AFP