Yes, you do.
Before we discuss further how important a surge protector is for a residential electrical system, we want to emphasize that there is nothing wrong with using power strips at the various outlets in your home. In fact, we encourage it. Multiple layers of defense against electrical surges are beneficial. You never want to overload an outlet in your house with an octopus plug: power strips allow you to plug in multiple items at a single outlet without the concern of tripping a circuit breaker because of a voltage spike.