A non-volatile memory device includes a substrate, an insulating layer on the substrate, and a plurality of serially connected resistive memory cells stacked in the insulating layer such that a first one of the plurality of resistive memory cells is on the substrate and a next one of the plurality of resistive memory cells is on the first one of the plurality of resistive memory cells to define a NAND-type resistive memory cell string. A bit line on the insulating layer is electrically connected to a last one of the plurality of resistive memory cells. At least one of the plurality of resistive memory cells may include a switching device and a data storage element including a variable resistor connected in parallel with the switching device. Related devices and fabrication methods are also discussed.