  We use the sample of emission-line nuclei derived from a recently completed
optical spectroscopic survey of nearby galaxies to quantify the incidence of
local (z = 0) nuclear activity. Consistent with previous studies, we find
detectable amounts of ionized gas in the central few hundred parsecs of most
(86%) galaxies. Half of the objects can be classified as H II or star-forming
nuclei and the other half as some form of AGN, of which we distinguish three
classes --- Seyfert nuclei, LINERs, and transition objects. The population of
AGNs consequently is very large; approximately 43% of the galaxies in our
survey can be regarded as "active." Most of the objects have much lower
luminosities than AGNs commonly studied; the median luminosity of the narrow
H-alpha line, after correcting for extinction, is only 2 x 10^39 erg/s. Our
sample therefore occupies the extreme faint end of the AGN luminosity function.
We detect signatures of a broad-line region, as revealed by visible broad
H-alpha emission, in $\sim$ 20% of the AGN sample. Seyfert nuclei, both type 1
and type 2, reside in $\sim$ 10% of all galaxies. LINERs make up the bulk
(1/2--3/4) of the AGN population and a significant fraction (1/5--1/3) of all
galaxies. A nonnegligible subset of LINERs emit broad H-alpha emission,
furnishing direct evidence that at least some LINERs are indeed related
physically to the AGN phenomenon. The dominant ionization mechanism of the
nuclear emission depends strongly on the morphological type and luminosity of
the host galaxy. AGNs are found predominantly in luminous, early-type (E to
Sbc) galaxies, while H II nuclei prefer less luminous, late-type (Sbc and
later) systems. The various AGN subclasses have broadly similar host galaxies.
