The frequency distributions of surface rain rate are evaluated in TRMM and SSM/I satellite observations and the NOAA/GFDL AM2 atmospheric general circulation model. Instantaneous satellite rain-rate observations averaged over the 2.5 deg. lat. × 2 deg. lon. model grid are shown to be representative of the half-hour rain rate from single time steps simulated by the model. Rain-rate events exceeding 10 mm h^-1 are observed by satellite in most regions, with 1 mm h^-1 events occurring more than 2 orders of magnitude more frequently than 10 mm h^-1 events. A model simulation using the relaxed Arakawa-Schubert (RAS) formulation of cumulus convection exhibits a strong bias toward many more light rain events compared to the observations and far too few heavy rain events. A simulation using an alternative convection scheme which includes an explicit representation of mesoscale circulations and an alternative formulation of the closure exhibits, among other differences, an order of magnitude more tropical rain events above the 5 mm h^-1 rate compared to the RAS simulation. This simulation demonstrates that global atmospheric models can be made to produce heavy rain events, in some cases even exceeding the observed frequency of such events. Additional simulations reveal that the frequency distribution of surface rain rate in the GCM is shaped by a variety of components within the convection parameterization, including the closure, convective triggers, the spectrum of convective and mesoscale clouds, and other parameters whose physical basis is currently understood to only a limited extent. Furthermore, these components interact nonlinearly such that the sensitivity of the rain-rate distribution to the formulation of one component may depend on the formulation of the others. Two simulations using different convection parameterizations are performed using perturbed sea surface temperatures as a surrogate for greenhouse-gas-forced climate warming. Changes in the frequency of heavy rain events associated with changing the convection scheme in the model are greater than the changes in the frequency of heavy rain events associated with a 2 K warming using either model. Improving the representation of the frequency distribution of rain rates will rely on refinements in the formulation of cumulus closure and the other components of convection schemes, and greater certainty in predictions of future changes in both total rainfall and in rain-rate distributions will require additional refinements in those parameterizations that determine the cloud and water-vapor feedbacks.