This is on the Stoneyfield Yogurt website:
"Is it safe to eat your (or any) yogurt after the date on the lid?
The date on the lid is a suggested sell-by date. It is not the date that the yogurt will expire or go bad. Up until this date, we feel that our yogurt will look and taste its best. It can be perfectly okay to eat yogurt after the sell-by date. Just use your judgment. If the yogurt looks, smells, and tastes good, and there are no visible signs of mold, it's okay to eat."
This is on the Dannon site:
"Because live and active cultures make yogurt what it is, check yogurt labels for these vital ingredients before you buy. Some yogurts have extremely low levels of cultures and others are heat-treated or pasteurized after culturing, destroying the cultures and their properties. DANNON ensures the presence of live and active cultures by pasteurizing their milk before cultures are added. Yogurt should be eaten within the week following the "sell by" date in order to take full advantage of the amount of live and active cultures present in the yogurt at the time of manufacture."
But that's more about eating when the live cultures are at their most active, not about the product being safe.