The Schottky barrier heights (SBHs) of defect-free interfaces of ZnO, CdO, MgO, and SrO with various metals and different terminations are investigated by density functional supercell calculations. The oxide bands are corrected for their density functional bandgap error by applying a U-type term to their metal-d and O-p states where necessary. The p-type SBHs are found to decrease linearly with increasing metal work function. The pinning factor S of the non-polar and polar interfaces is similar for each oxide. S is found to be 0.26, 0.56, 0.74, and 0.96 for CdO, ZnO, MgO, and SrO, respectively, with S increasing with increasing oxide ionicity. The calculated pinning factors are generally consistent with the metal-induced gap state model in terms of variation in ionicity and dielectric constant. A significant shift of SBHs from the non-polar to the polar interfaces of 0.4, 1, and 0.5 eV for ZnO, MgO, and SrO, respectively, is found, which can be explained by an interfacial dipole. Our results are also useful to describe Co,Fe|MgO interfaces in magnetic tunnel junctions.