Rugs and carpeting made from synthetic fibers won't grow mold or mildew. Keep things clean. Regularly wash down areas where mildew frequently grows. This includes cement walls and floors, bathrooms and around washers and dryers. Paint basement walls with mildew resistant paint or add mildew-resistant paneling.
Latex paints are also mildew resistant.
Seal basement wood floors and furniture to prevent mildew growth. Sealers such as varnish and polyurethane prevent moisture from seeping into wood. Reorganize storage areas. Remove old clothing from closets and boxes, wash and repack elsewhere. Control those odors for good.