Transistors are the basis for electronic switching and memory devices as they exhibit extreme reliabilities with on/off ratios of 10(4)-10(5), and billions of these three-terminal devices can be fabricated on single planar substrates. On the other hand, two-terminal devices coupled with a nonlinear current-voltage response can be considered as alternatives provided they have large and reliable on/off ratios ratios and that they can be fabricated on a large scale using conventional or easily accessible methods. Here, we report that two-terminal devices consisting of discontinuous 5-10 nm thin films of graphitic sheets grown by chemical vapour deposition on either nanowires or atop planar silicon oxide exhibit enormous and sharp room-temperature bistable current-voltage behaviour possessing stable, rewritable, non-volatile and non-destructive read memories with on/off ratios of up to 10(7) and switching times of up to 1 mu s (tested limit). A nanoelectromechanical mechanism is proposed for the unusually pronounced switching behaviour in the devices.