Cathodoluminescence spectra have been measured to determine the characteristics of ubiquitous green luminescence (GL) in nonstoichiometric zinc oxide (ZnO). Zn- and O-rich ZnO were found to exhibit characteristic emissions at 2.53 eV [full width at half-maximum (FWHM) 340 meV] and 2.30 eV (FWHM 450 meV), respectively. Hydrogen was used to probe the physical nature of GL centers. The Zn-rich GL is enhanced upon H incorporation, whereas the O-rich GL is completely quenched as its underlying acceptor-like $V_{\mathrm{Zn}}$ centers are passivated by H. The GL emission bands each exhibit remarkably different excitation-power dependencies. The Zn-rich GL follows a close to linear relationship with excitation power, while the O-rich GL exhibits a square-root dependence. Calculations based on bimolecular recombination equations show the defect concentration in Zn-rich ZnO is three orders of magnitude greater than that in O-rich ZnO, indicating $V_{\mathrm{O}}$ is more readily formed than $V_{\mathrm{Zn}}$ in thermochemical treatments of ZnO.