A new survey of muonium states brings the total of binary non-magnetic oxides studied to 30, with normal muonium—the interstitially trapped atomic state—found in 15 of these. The number of shallow-donor states of the type known in ZnO now also totals 15, but there are hints of several others. Tantalizingly, the shallow-donor and deep-atomic states are found to coexist in several of the candidate high-permittivity dielectrics. Highly anisotropic states, resembling anomalous muonium in semiconductors and including examples of muonium trapped at oxygen vacancies, complete a spectrum of hyperfine parameters covering five powers of ten. Effective ionization temperatures range from 10 K for shallow to over 1000 K for deep states, with corresponding activation energies between several meV and several eV. The oxide band gap emerges as a parameter controlling the systematics of the deep-to-shallow transition for muonium and, by inference, monatomic hydrogen.