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The rate of decay of metastable states of Josephson systems is determined for a wide range of parameters. The temperature extends from the region where the decay is thermally activated down to very low temperatures where the system decays by macroscopic quantum tunneling. The range of damping parameters extends from weakly damped to heavily overdamped motions. It is found that the transition between thermally activated decay and tunneling occurs near a cross over temperature T0 which decreases with increasing damping strength. Well above T0 the rate follows the classical Arrhenius law where the preexponential factor is affected by the frequency dependent damping. As T0 is approached, quantum corrections to the classical rate become increasingly important. In the vicinity of T0 the rate follows a scaling law describing the crossover between thermally activated and quantum mechanical decay. In the region below T0 the decay rate can be determined analytically only in limiting cases. For systems described by the resistively shunted junction model, numerical calculations are presented. The results are compared with recent experimental data on the decay of the zero-voltage state in current biased Josephson junctions and on fluxoid quantum transitions in SQUID rings.