First-principles electronic structure calculations are presented on a variety of Au compounds and species--encompassing a wide range of formal oxidation states, coordination geometries, and chemical environments--in order to understand the potentially systematic behavior in the nature and energetics of d states that are implicated in catalytic activity. In particular, we monitor the position of the d-band center, which has been suggested to signal catalytic activity for reactions such as CO oxidation. We find a surprising absence of any kind of correlation between the formal oxidation state of Au and the position of the d-band center. Instead, we find that the center of the d band displays a nearly linear dependence on the degree of its filling, and this is a general relationship for Au irrespective of the chemistry or geometry of the particular Au compound. Across the compounds examined we find that even small calculated changes in the d-band filling result in a relatively large effect on the position of the d-band center. The results presented here have some important implications for the question of the catalytic activity of Au and indicate that the formal oxidation state is not a determining factor.