Oxygen abundances are obtained by optical spectrophotometry of H II regions in seven nearby dwarf irregular galaxies. All of these yield oxygen abundances of less than 1/10 of the solar value, and most are in the range of 3-5 percent of the solar value. This suggests that observations of nearby dwarf galaxies may provide an effective means for studying the chemical evolution of low-mass galaxies and, possibly, the primordial helium abundance. A strong correlation is found between the oxygen abundances and absolute magnitudes for nearby irregular galaxies. This correlation will be useful for estimating abundances of irregular galaxies without observable H II regions, and possibly as a distance indicator for irregular galaxies with known abundances. It is inferred from this relationship that infall is no more important in irregular galaxies with extremely large H I halos than in typical irregular galaxies. 72 refs.