We investigate the fundamental limit of radiative cooling of objects on the Earth's surfaces under general conditions including nonradiative heat transfer. We deduce the lowest steady-state temperature attainable and highest net radiative cooling power density available as a function of temperature. We present the exact spectral emissivity that can reach such limiting values, and show that the previously used 8-13 mu m atmospheric window is highly inappropriate in low-temperature cases. The critical need for materials with simultaneously optimized optical and thermal properties is also identified. These results provide a reference against which radiative coolers can be benchmarked.