There's all kinds of boxing equipment, and once people starting training, they find a whole lot of it at their disposal. All boxers do not use all of the equipment available. Often it depends on what the boxer's goals are and their personal preferences. There are some pieces of equipment that have to be used in certain situations. Like for example, wearing a mouth guard is a must when sparring and during actual matches.
Most gyms have bags, jump ropes, etc. But when looking for items like mouth guards and hand wraps, sporting goods stores don't appear to carry a wide variety. In my experience, I've had better luck buying directly from boxing equipment dealers, such as Everlast, Ringside, and Title.
For details about various boxing equipment, check these pages out: