The formation energy, structural relaxation, and defect induced states of neutral anion vacancies of five oxides (i.e., MgO, Al2O3, ZnO, In2O3, and SnO2) and four nitrides (i.e., AlN, Si3N4 Ge3N4, and InN) are systematically discussed, based on first-principles plane-wave pseudopotential calculations. Two types of polymorphs for each compound are compared. The number of atoms included in the supercells ranged from 54 to 96. When a localized vacancy-induced state appears within the band gap, as in a typical ionic crystal, the formation energy can be well scaled by the band gap of the perfect crystal. On the other hand, when an empty and localized vacancy-induced state is located above the highest occupied band or no localized state is formed, the formation energy has a tendency to be smaller. In compounds such as ZnO and SnO2, the formation energy is dependent largely on the crystal structure. This result can be explained by the transition of the vacancy-induced state from occupied to unoccupied, which is caused by the change in atomic arrangement, as represented by the cation coordination number.