Branching point process models such as the epidemic-type aftershock sequence (ETAS) models introduced by Ogata (1988, 1998) are often used in the description, characterization, simulation, and declustering of modern earthquake catalogs. The present work investigates how the parameters in these models vary across different tectonic zones. After considering divisions of the surface of the Earth into several zones based on the plate-boundary model of Bird (2003), ETAS models are fit to the occurrence times and locations of shallow earthquakes within each zone. Computationally, the expectation-maximization (EM) type algorithm of Veen and Schoenberg (2008) is employed for the purpose of model fitting. The fits and variations in parameter estimates for distinct zones are compared, and seismological implications are discussed. In particular, we find that estimated background seismicity rates range by a factor of nearly 500 for interplate and trench events, respectively; the estimated productivity parameter, governing the relationship between the magnitude of an earthquake and its expected number of direct aftershocks, ranges by a factor of more than five from events in the slow-moving zone to events in active continental areas, suggesting a much higher rate of swarming in the ridges than in the trenches and active continental zones. Despite the pronounced differences between the seismicity patterns and parameter estimates in the different zones, the ETAS model with few parameters and with the same functional form seems to fit reasonably well to the seismicity in each zone.