Room-temperature ferromagnetism is observed in (110) oriented ZnO films made from targets containing 5 at.% of Sc, Ti, V, Fe, Co, or Ni, but not Cr, Mn, or Cu ions. There are large moments, 2.6 μ B and 0.5 μ B/dopant atom for Co-and Ti-containing oxides, respectively. There is also a moment of 0.3 μ B/S c. Magnetization is very anisotropic, with variations of up to a factor of 3 depending on the orientation of the applied field relative to the substrate. Results are interpreted in terms of a spin-split donor impurity-band model, which can account for ferromagnetism in insulating or conducting high-k oxides with concentrations of magnetic ions that lie far below the percolation threshold. Magnetic moments are associated with two-electron defects in the films as well as unpaired electrons of the 3 d ions.