Wide band gap oxides are versatile materials with numerous applications in research and technology. Many properties of these materials are intimately related to defects with the most important defect being the oxygen vacancy. Here, using electronic structure calculations, we show that the charge transition level (CTL) and eigenstates associated with oxygen vacancies, which to a large extent determine their electronic properties, are confined to a rather narrow energy range, even while band gap and the electronic structure of the conduction band vary substantially. Vacancies are classified according to their character (deep vs shallow), which shows that the alignment of electronic eigenenergies and CTL can be understood in terms of the transition between cavity-like localized levels in the large band-gap limit and strong coupling between conduction band and vacancy states for small to medium band gaps. We consider both conventional and hybrid functionals and demonstrate that the former yields results in very good agreement with the latter provided that band-edge alignment is taken into account.