We analyse HST surface brightness profiles for 143 early-type galaxies in the Virgo and Fornax Clusters. Sersic models provide accurate descriptions of the global profiles with a notable exception: the observed profiles deviate systematically inside
a characteristic break radius of R_b ~ 0.02R_e where R_e is the effective radius of the galaxy. The sense of the deviation is such that bright galaxies (M_B < -20) typically show central light deficits with respect to the inward extrapolation of the Sersic model, while the great majority of low- and intermediate-luminosity galaxies (-19.5 < M_B < -15) show central light excesses; galaxies occupying a narrow range of intermediate luminosities (-20 < M_B < -19.5) are usually well fitted by Sersic models over all radii. The slopes of the central surface brightness profiles, when measured at fixed fractions of R_e, vary smoothly as a function of galaxy luminosity in a manner that depends sensitively on the choice of measurement radius. We show that a recent claim of strong bimodality in slope is likely an artifact of the galaxy selection function used in that study. To provide a more robust characterization of the inner regions of galaxies, we introduce a parameter that describes the central luminosity deficit or excess relative to the inward extrapolation of the outer Sersic model. We find that this parameter varies smoothly over the range of ~ 720 in blue luminosity spanned by the Virgo and Fornax sample galaxies, with no evidence for a dichotomy. We argue that the central light excesses (nuclei) in M_B > -19 galaxies may be the analogs of the dense central cores that are predicted by some numerical simulations to form via gas inflows. (ABRIDGED)
