We use a comprehensive database of black hole masses (M-BH) and nuclear luminosities to investigate the relationship between radio emission and M-BH. Our sample covers a wide range of nuclear activity, from nearby inactive nuclei to classical Seyfert 1 nuclei and luminous quasars. Contrary to some previous studies, we find that the radio continuum power, either integrated for the entire galaxy or isolated for the core, correlates poorly with M-BH. The degree of nuclear radio loudness, parameterized by the radio-to-optical luminosity ratio R, also shows no clear dependence on M-BH. Radio-loud nuclei exist in galaxies with a wide range of M-BH, from similar to10(6) to a few times 10(9) M-., and in a variety of hosts, from disk-dominated spiral to giant elliptical galaxies. We demonstrate that R is strongly inversely correlated with L/L-E, the ratio of nuclear luminosity to the Eddington luminosity, and hence with the mass accretion rate. Most or all of the weakly active nuclei in nearby galaxies are radio-loud, highly sub-Eddington systems that are plausibly experiencing advection-dominated accretion.