VI curves of resistively shunted single Josephson junctions with different capacitances and tunneling resistances are found to display a crossover between two types of VI curves: one without and another with a resistance bump (negative second derivative) at zero bias. The crossover corresponds to the dissipative phase transition (superconductor-insulator transition) at which macroscopic quantum tunneling delocalizes the Josephson phase and destroys superconductivity. Our measured phase diagram does not agree with the diagram predicted by the original theory, but does coincide with a theory that takes into account the accuracy of voltage measurements and thermal fluctuations.