The one piece of equipment that is absolutely vital in boxing and other similar combat sports is the mouth guard. It is the most important for one reason. Your teeth are valuable, and you only get one adult set. Without a mouthguard, you may find yourself easily toothless. Gloves allow a person to punch with full power with less risk of injuring their hands. This means they are able to punch you full power in the mouth without risk.
One should never spar or do any contact without a mouth guard as that can easily set you back many thousands of dollars trying to fix your now missing teeth. In addition, it also has the benefit of absorbing some of the shock from blows.