O.K., classic Caesar salad dressing includes anchovy. And, you are thinking...no way! I agree that anchovy is a strong flavor disliked by many (including me). But in this recipe the anchovy adds a subtle flavor that you really can not identify.
You can leave the anchovy out if you must, but it will not be a classic Caesar Salad without them. As mentioned, they add so much flavor and most people do not even know they are there.