We present optically-pumped emission data for ZnO, showing that high excitation effects and stimulated emission / lasing are observed in nanocrystalline ZnO thin films at room temperature, although such effects are not seen in bulk material of better optical quality. A simple model of exciton density profiles is developed which explains our results and those of other authors. Inhibition of exciton diffusion in nanocrystalline samples compared to bulk significantly increases exciton densities in the former, leading, via the nonlinear dependence of emission in the exciton bands on the pump intensity, to large increases in emission and to stimulated emission.