Programmable memory devices having a cross-point array of polymer junctions with individually-programmed conductances are provided. In one aspect, a method of forming a memory device includes: forming first metal lines on an insulating substrate; forming polymeric resistance elements on the first metal lines; and forming second metal lines over the polymeric resistance elements with a single one of the polymeric resistance elements present at each intersection of the first/second metal lines forming a cross-point array. A memory device and a method of operating a memory device are also provided.