Narrow gaps are formed in suspended single to few layer graphene devices using a pulsed electrical breakdown technique. The conductance of the resulting devices can be programmed by the application of voltage pulses, with a voltage of 2.5V~4.5V corresponding to an ON pulse and voltages ~8V corresponding to OFF pulses. Electron microscope imaging of the devices shows that the graphene sheets typically remain suspended and that the device conductance tends to zero when the observed gap is large. The switching rate is strongly temperature dependent, which rules out a purely electromechanical switching mechanism. This observed switching in suspended graphene devices strongly suggests a switching mechanism via atomic movement and/or chemical rearrangement, and underscores the potential of all-carbon devices for integration with graphene electronics.