This paper presents the results of a high resolution radio imaging survey of all known ( 96 ) low-luminosity active galactic nuclei ( LLAGNs ) at D \leq 19 Mpc . We first report new 2 cm ( 150 mas resolution using the VLA ) and 6 cm ( 2 mas resolution using the VLBA ) radio observations of the previously unobserved nuclei in our samples and then present results on the complete survey . We find that almost half of all LINERs and low-luminosity Seyferts have flat-spectrum radio cores when observed at 150 mas resolution . Higher ( 2 mas ) resolution observations of a flux-limited subsample have provided a 100 % ( 16 of 16 ) detection rate of pc-scale radio cores , with implied brightness temperatures \ga 10 ^ { 8 } K. The five LLAGNs with the highest core radio fluxes also have pc-scale ‘ jets. ’ Compact radio cores are almost exclusively found in massive ellipticals and in type 1 nuclei ( i.e . nuclei with broad H \alpha emission ) . Only a few ‘ transition ’ nuclei have compact radio cores ; those detected in the radio have optical emission-line diagnostic ratios close to those of LINERs/Seyferts . This indicates that some transition nuclei are truly composite Seyfert/LINER+H II region nuclei , with the radio core power depending on the strength of the former component . The core radio power is correlated with the nuclear optical ‘ broad ’ H \alpha luminosity , the nuclear optical ‘ narrow ’ emission-line luminosity and width , and with the galaxy luminosity . In these correlations LLAGNs fall close to the low-luminosity extrapolations of more powerful AGNs . The scalings suggest that many of the radio-non-detected LLAGNs are simply lower power versions of the radio-detected LLAGNs . The ratio of core radio power to nuclear optical emission-line luminosity increases with increasing bulge luminosity for all LLAGNs . Also , there is evidence that the luminosity of the disk component of the galaxy is correlated with the nuclear emission-line luminosity ( but not the core radio power ) . About half of all LLAGNs with multiple epoch data show significant inter-year radio variability . Investigation of a sample of \sim 150 nearby bright galaxies , most of them LLAGNs , shows that the nuclear ( \leq 150 mas size ) radio power is strongly correlated with both the black hole mass and the galaxy bulge luminosity ; linear regression fits to all \sim 150 galaxies give : log P _ { 2 cm } = 1.31 ( \pm 0.16 ) log M _ { MDO } + 8.77 and log P _ { 2 cm } = 1.89 ( \pm 0.21 ) log L _ { B } ( bulge ) - 0.17 . Low accretion rates ( \leq 10 ^ { -2 } -10 ^ { -3 } of the Eddington rate ) are implied in both advection- and jet-type models . In brief , all evidence points towards the presence of accreting massive black holes in a large fraction , perhaps all , of LLAGNs , with the nuclear radio emission originating in either the accretion inflow onto the massive black hole or from jets launched by this black hole - accretion disk system .