  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)
