Idealized general circulation models (GCMs) suggest global-mean precipitation ceases to increase with warming in hot climates. However, it is unclear if this occurs in more comprehensive GCMs. Here, we examine precipitation over a wide range of climates simulated with comprehensive GCMs. We find that in the Community Atmosphere Model, global-mean precipitation increases approximately linearly with global-mean surface temperatures up to about 330~K, where it peaks at 5~mm~day$^{-1}$. Beyond 330~K, global-mean precipitation decreases substantially despite increasing surface temperatures. This occurs because of increased atmospheric shortwave absorption from water vapor, which limits shortwave radiation available for surface evaporation. Precipitation decreases in the tropics and subtropics, but continues to increase in the extratropics due to increased poleward moisture transport. Precipitable water increases everywhere, resulting in longer water-vapor residence times and implying more episodic precipitation. Other GCMs indicate global-mean precipitation might exhibit a smaller maximum rate and begin to decrease at lower surface temperatures.