Baking soda (sodium bicarbonate) has long been used as a natural cleanser and deodorizer. We use it to get burned gunk off pots and pans, to clean stainless steel without scratching it and to clean microwaves without leaving unpleasant chemical traces. It also cuts odors in cat litter boxes, and people often leave an opened box of baking soda in the refrigerator because it absorbs nasty odors. In addition, baking soda was one of the first tooth cleaning products. Many people also add it to bath water for gentle, relaxing cleansing.
So it only makes sense that some people have found that baking soda also cuts through armpit odors. It doesn't stop you from perspiring, but its neutralizing and buffering properties break the sweat down from bacteria food into something more like water. Some people dust liberally with baking soda after showering. Others suggest putting baking soda on a clean, wet washcloth and then applying that to the underarms.
Others report success with baby powder, supplemented by baby wipes during the day. Baby powder can help reduce wetness, and it has a pleasant smell. Be careful, though, to avoid remedies that suggest mixing baking soda with cornstarch, or using baby powders made with cornstarch rather than talc. Those odor-causing bacteria love to feed on starch [source: Feldman].