The discovery of a large number of terrestrial exoplanets in the habitable zones of their stars, many of which are qualitatively different from Earth, has led to a growing need for fast and flexible 3D climate models, which could model such planets and explore multiple possible climate states and surface conditions. We respond to that need by creating ExoPlaSim, a modified version of the Planet Simulator (PlaSim) that is designed to be applicable to synchronously rotating terrestrial planets, planets orbiting stars with non-solar spectra, and planets with non-Earth-like surface pressures. In this paper we describe our modifications, present validation tests of ExoPlaSims performance against other GCMs, and demonstrate its utility by performing two simple experiments involving hundreds of models. We find that ExoPlaSim agrees qualitatively with more-sophisticated GCMs such as ExoCAM, LMDG, and ROCKE-3D, falling within the ensemble distribution on multiple measures. The model is fast enough that it enables large parameter surveys with hundreds to thousands of models, potentially enabling the efficient use of a 3D climate model in retrievals of future exoplanet observations. We describe our efforts to make ExoPlaSim accessible to non-modellers, including observers, non-computational theorists, students, and educators through a new Python API and streamlined installation through pip, along with online documentation.