Spontaneous formation of stable molecular wires between a gold scanning tunneling microscopy (STM) tip and substrate is observed when the sample has a low coverage of alpha,omega-dithiol molecules and the tunneling resistance is made sufficiently small. Current-distance curves taken under these conditions exhibit characteristic current plateaux at large tip-substrate separations from which the conductivity of a single molecule can be obtained. The versatility of this technique is demonstrated using redox-active molecules under potential control, where substantial reversible conductivity changes from 0.5 to 2.8 nS were observed when the molecule was electrochemically switched from the oxidized to the reduced state.