Megaconstellations of thousands to tens of thousands of artificial satellites are rapidly being developed and launched. These satellites have the potential to substantially impact observational astronomy research worldwide, particularly for wide-field imaging of small bodies. Here we provide predictions for the optical brightnesses and on-sky distributions of several megaconstellations, including Starlink, OneWeb, Kuiper, and StarNet/GW, for a total of 65,000 satellites on their filed or predicted orbits. We use a simple model of satellite reflectivity, which we calibrate using published Starlink observations. We use this model to estimate the visible magnitudes and on-sky distributions for these satellites at different places on Earth, in different seasons, and different times of night. We also make predictions for bright satellite observation rates for a few observatories around the world. Without significant mitigation addressing single-satellite and cumulative impacts, these satellite megaconstellations will have far-reaching consequences for research astronomy worldwide, with latitudes near 50 degrees North and South being most severely affected.