We assess the spatial distribution of the largest rainfall‐generated streamflows from a database of 35,663 flow records composed of the largest 10% of annual peak flows from each of 14,815 U.S. Geological Survey stream gaging stations in the United States and Puerto Rico. High unit discharges (peak discharge per unit contributing area) from basins with areas of 2.6 to 26,000 km² (1–10,000 mi²) are widespread, but streams in Hawaii, Puerto Rico, and Texas together account for more than 50% of the highest unit discharges. The Appalachians and western flanks of Pacific coastal mountain systems are also regions of high unit discharges, as are several areas in the southern Midwest. By contrast, few exceptional discharges have been recorded in the interior West, northern Midwest, and Atlantic Coastal Plain. Most areas of high unit discharges result from the combination of (1) regional atmospheric conditions that produce large precipitation volumes and (2) steep topography, which enhances precipitation by convective and orographic processes and allows flow to be quickly concentrated into stream channels. Within the conterminous United States, the greatest concentration of exceptional unit discharges is at the Balcones Escarpment of central Texas, where maximum U.S. rainfall amounts apparently coincide with appropriate basin physiography to produce many of the largest measured U.S. floods. Flood‐related fatalities broadly correspond to the spatial distribution of high unit discharges, with Texas having nearly twice the average annual flood‐related fatalities of any other state.