We analyze brightness profiles for 143 early-type galaxies in the Virgo and Fornax Clusters, observed with the Advanced Camera for Surveys on the Hubble Space Telescope. Sérsic models are found to provide accurate representations of the global profiles with a notable exception: the observed profiles deviate systematically inside a characteristic ''break'' radius of R b % 0:02 þ0:025 À0:01 R e , where R e is the effective radius of the galaxy. The sense of the deviation is such that bright galaxies (M B P À 20) typically show central light deficits with respect to the inward extrapolation of the Sérsic model, while the great majority of low-and intermediate-luminosity galaxies (À19:5 P M B P À 15) show central light excesses; galaxies of intermediate luminosities (À20 P M B P À 19:5) are generally well fitted by Sérsic models over all radii. We show that the slope, 0 , of the central surface brightness profiles, when measured at fixed fractions of R e , varies smoothly as a function of galaxy luminosity in a manner that depends sensitively on the choice of measurement radius. We find no evidence for a core/power-law dichotomy, and show that a recent claim of strong bimodality in 0 is likely an artifact of the biased galaxy selection function used in that study. To provide a more robust characterization of the inner regions of galaxies, we introduce a parameterwhere L g and L S are the integrated luminosities inside 0:02R e of the observed profile and of the inward extrapolation of the outer Sérsic model -to describe the central luminosity deficit (Á 0:02 < 0) or excess (Á 0:02 > 0). We find that Á 0:02 varies smoothly over the range of %720 in luminosity spanned by the sample galaxies, with again no evidence for a dichotomy. We argue that the central light excesses in M B k À 19 galaxies may be the analogs of the dense central cores predicted by some numerical simulations to form via gas inflows.