The outcome of impacts onto and between icy planetary bodies is controlled by the material response defined by the shock Hugoniot. New Lagrangian shock wave profile measurements in H2O ice at initial temperatures (T0) of 100 K, together with previous T0 = 263 K data, define five distinct regions on the ice Hugoniot: elastic shocks in ice Ih, ice Ih deformation shocks, and shock transformation to ices VI, VII and liquid water. The critical pressures required to induce incipient melting (0.6, 4.5 GPa) and complete melting (3.7, >5.5 GPa) upon isentropic release from the shock state (for T0 = 263, 100 K) were revised using calculated shock temperatures and entropy. On account of the >40% density increase upon transformation from ice Ih to ices VI and VII, the critical shock pressures required for melting are factors of 2 to 5 lower than earlier predicted. Consequently, hypervelocity impact cratering on planetary surfaces and mutual collisions between porous cometesimals will result in abundant shock-induced melting throughout the solar system.