The ACS Virgo Cluster Survey is a Hubble Space Telescope program to obtain high-resolution imaging in widely separated bandpasses (F475W ≈ g and F850LP ≈ z) for 100 early-type members of the Virgo Cluster, spanning a range of 460 in blue luminosity. We use this large, homogenous data set to examine the innermost structure of these galaxies and to characterize the properties of their compact nuclei. We present a sharp upward revision in the frequency of nucleation in early-type galaxies brighter than M_B ≈ -15 (66% ≾ f_n ≾ 82%) and show that ground-based surveys underestimated the number of due to surface brightness selection effects, limited sensitivity and poor spatial resolution. We speculate that previously reported claims that nucleated dwarfs are more concentrated toward the center of Virgo than their nonnucleated counterparts may be an artifact of these selection effects. There is no clear evidence from the properties of the nuclei, or from the overall incidence of nucleation, for a change at M_B ~ -17.6, the traditional dividing point between dwarf and giant galaxies. There does, however, appear to be a fundamental transition at M_B ~ -20.5, in the sense that the brighter, core-Sersic galaxies lack resolved (stellar) nuclei. A search for that may be offset from the photocenters of their host galaxies reveals only five candidates with displacements of more than 05, all of which are in dwarf galaxies. In each case, however, the evidence suggests that these nuclei are, in fact, globular projected close to the galaxy photocenter. Working from a sample of 51 galaxies with prominent nuclei, we find a median half-light radius of (r_h) = 4.2 pc, with the sizes of individual ranging from 62 pc down to ≤2 pc (i.e., unresolved in our images) in about a half-dozen cases. Excluding these unresolved objects, the sizes are found to depend on luminosity according to the relation r_h α L ^(0.50±0.03). Because the large majority of are resolved, we can rule out low-level AGNs as an explanation for the luminosity excess in almost all cases. On average, the are ≈3.5 mag brighter than a typical globular cluster. Based on their broadband colors, the appear to have old to intermediate age stellar populations. The colors of the in galaxies fainter than M_B ≈ -17.6 are tightly correlated with their luminosities, and less so with the luminosities of their host galaxies, suggesting that their chemical enrichment histories were governed by local or internal factors. Comparing the to the nuclear clusters found in late-type spiral galaxies reveals a close match in terms of size, luminosity, and overall frequency. A formation mechanism that is rather insensitive to the detailed properties of the host galaxy properties is required to explain this ubiquity and homogeneity. The mean of the frequency function for the nucleus-to-galaxy luminosity ratio in our nucleated galaxies, (log η) = -2.49 ± 0.09 dex (σ = 0.59 ± 0.10), is indistinguishable from that of the SBH-to-bulge mass ratio, log(M/M_(gal) = -2.61 ± 0.07 dex (σ = 0.45 ± 0.09), calculated in 23 early-type galaxies with detected supermassive black holes (SBHs). We argue that the compact stellar found in many of our program galaxies are the low-mass counterparts of the SBHs detected in the bright galaxies. If this interpretation is correct, then one should think in terms of central massive objects—either SBHs or compact stellar nuclei—that accompany the formation of almost all early-type galaxies and contain a mean fraction ≈0.3% of the total bulge mass. In this view, SBHs would be the dominant formation mode above M_B ≈ -20.5.