Damp basement flooring in conjunction with organic flooring, such as wood, is a breeding ground for mold. This mold causes a musty smell, and releases harmful airborne contaminants. So instead of using wood in your basement, use inorganic carpet tiles, vinyl, or false flooring. Since organic material is food for mold, choose carpet tiles made up of inorganic materials. Options exist that can be individually removed for cleaning purposes, and at the same time serve as a vapor barrier and insulation. Vinyl flooring is another option. With vinyl, the same flooring you may use in your kitchen is not what you’ll use in your basement. Special vinyl tiles are made which provide insulation and a vapor barrier, and these should be used. If your basement is deep enough, lay 1.5″ to 2″ polystyrene foam directly onto the basement floor. Polystyrene doesn’t rot, and it insulates against the cold. You can apply plywood on top of the polystyrene, then screw directly into concrete using fasteners. Finish this job with your choice of floor coverings.