We report on the one-photon photoluminescence of gold nanorods with different aspect ratios. We measured photoluminescence and scattering spectra from 82 gold nanorods using single-particle spectroscopy. We found that the emission and scattering spectra closely resemble each other independent of the nanorod aspect ratio. We assign the photoluminescence to the radiative decay of the longitudinal surface plasmon generated after fast interconversion from excited electron-hole pairs that were initially created by 532 nm excitation. The emission intensity was converted to the quantum yield and was found to approximately exponentially decrease as the energy difference between the excitation and emission wavelength increased for gold nanorods with plasmon resonances between 600 and 800 nm. We compare this plasmon emission to its molecular analogue, fluorescence.