An aluminum-free antiperspirant/deodorant composition in the form of stick, cream, or flowable gel includes a carrier that includes a polyhydric alcohol or is a mixture of a polyhydric alcohol and water; a thickening agent including a C14-22 fatty acid salt; and an antiperspirant active and optionally a film-forming polymer dispersed in the carrier. The antiperspirant active is primarily a zinc-based antiperspirant active.