1. A memory device, comprising: read circuits coupled to a plurality of memory elements that are programmable between at least two different resistance states, the read circuits generating output values based on resistance states of selected memory elements in a read operation; and current limit circuits that limit a current flow through each memory element to less than a program threshold current in the read operation, the current limit circuits being connected in series with the selected memory elements between the read circuits and a predetermined voltage; wherein the program threshold current corresponds to a current that flows through a memory element being programmed to cause its resistance to change to a resistance between that of two different resistance states.