Nuclear star clusters (NSCs) are compact stellar systems that inhabit the central regions of many galaxies, including the Milky Way. They tend to be larger and more massive than the typical globular cluster but, remarkably, their central stellar surface densities can be even more extreme. I will present an investigation on the occurrence and prominence of NSCs in a volume-limited sample of nearly 400 quiescent galaxies in the core of the Virgo cluster spanning seven decades in stellar mass. The fraction of nucleated galaxies depends strongly on galaxy mass, with a peak around 1E9 Msun and a monotonic decline toward lower masses. The NSC-to-galaxy mass ratio is also a highly non-linear function that floors at about the same characteristic stellar mass. NSCs in both more and less massive galaxies are much more prominent--but the scatter at fixed mass is nearly half a dex, probably reflecting the stochastic nature of NSC growth. Finally, I will discuss the implications of these results for models of NSC formation, and the connection with their host galaxies and other star cluster systems.