Room-temperature free exciton absorption and luminescence are observed in ZnO thin films grown on sapphire substrates by the laser molecular beam epitaxy technique. At moderate optical pumping intensities, an exciton-exciton collision induced stimulated emission peak is observed at 390 nm. The existence of this peak is related to the presence of closely packed hexagonally shaped microcrystallites in these films. Stimulated emission due to electron-hole plasma recombination process is also observed at higher pumping intensities.