Yes, every bathroom should have an exhaust fan. Your bathroom is the wettest room in your home, i.e. sweaty windows, peeling wallpaper, steamy showers, flushing toilets and running sinks, mold and mildew, equal high humidity. And with major moisture comes potential problems.
The good news is that proper bathroom ventilation will keep the humidity low. Bathroom fans come in various shapes, sizes and styles that correspond to their features and the size of the bathroom where it will be used.