We provide estimates of volcanism versus time for planets with Earth-like composition and masses 0.25-25 M _⊕, as a step toward predicting atmospheric mass on extrasolar rocky planets. Volcanism requires melting of the silicate mantle. We use a thermal evolution model, calibrated against Earth, in combination with standard melting models, to explore the dependence of convection-driven decompression mantle melting on planet mass. We show that (1) volcanism is likely to proceed on massive planets with plate tectonics over the main-sequence lifetime of the parent star; (2) crustal thickness (and melting rate normalized to planet mass) is weakly dependent on planet mass; (3) stagnant lid planets live fast (they have higher rates of melting than their plate tectonic counterparts early in their thermal evolution), but die young (melting shuts down after a few Gyr); (4) plate tectonics may not operate on high-mass planets because of the production of buoyant crust which is difficult to subduct; and (5) melting is necessary but insufficient for efficient volcanic degassing—volatiles partition into the earliest, deepest melts, which may be denser than the residue and sink to the base of the mantle on young, massive planets. Magma must also crystallize at or near the surface, and the pressure of overlying volatiles must be fairly low, if volatiles are to reach the surface. If volcanism is detected in the 10 Gyr-old τ Ceti system, and tidal forcing can be shown to be weak, this would be evidence for plate tectonics.