Always trust your nose!
The "best by" date is a useful reference, but it's somewhat arbitrary and may not be consistent among different producers. Eggs might be perfectly safe after that date, but eggs can also go bad well before their "best by" date, if for example, they weren't maintained at the proper temperature.
Eggs can be dangerous, but still smell perfectly fine. However, if your nose detects even the slightest hint of a suspicious odor, it's not worth taking the chance of cooking with them. In addition to the possibility of getting sick, the spoiled egg could ruin the flavor of whatever you are baking.
When shopping for eggs...
... look for the production date code. This three-digit number identifies the day of the year the eggs were packaged. For example, the eggs on the left were packaged on March 14th, and the eggs on the right were packaged on February 19th:
To buy the freshest eggs, simply choose the package with the highest number (until January, when it starts back at 001 again).