In order to elucidate room-temperature (RT) ferromagnetism (FM) in ZnO, we have analyzed a multitude of experimental publications with respect to the ratio of grain-boundary (GB) area to grain volume. FM only appears if this ratio exceeds a certain threshold value $s_{\text{th}}$. Based on these important results nanograined pure and Mn-doped ZnO films have been prepared, which reveal reproducible RT FM and magnetization proportional to the film thickness, even for pure ZnO films. Our findings strongly suggest that grain boundaries and related vacancies are the intrinsic origin for RT ferromagnetism.