Results on four ferromagnetic systems which contradict the accepted paradigms of localized or band magnetism are reviewed. The systems—irradiated graphite, nonstoichiometric CaB₆, thin films of HfO₂, and doped nonmagnetic oxides—all have small ferromagnetic moments and Curie points well above room temperature despite the absence of atoms with partially filled d or f shells. Parasitic ferromagnetic impurity phases are not a general explanation. A common feature is the presence of lattice or bond defects, which can give rise to an impurity band. Some of the ways in which this impurity band may become spin-polarized are discussed.