The emission spectrum of individual high-quality ZnO nanowires consists of a series of Fabry-Pérot-like eigenmodes that extend far below the band gap of ZnO. Spatially resolved luminescence spectroscopy shows that light is emitted predominantly at both wire ends, with identical spectra reflecting standing wave polariton eigenmodes. The intensity of the modes increases supralinearly with the excitation intensity, indicating that the mode population is governed by scattering among polaritons. Due to strong light-matter interaction, light emission from a ZnO nanowire is not dictated by the electronic band diagram of ZnO but depends also on the wire geometry and the excitation intensity. Delocalized polaritons provide a natural explanation for the pronounced subwavelength guiding in ZnO wires that has been reported previously.