We present images of the HCN J = 1-0 emission from five nearby spiral galaxies made with the Berkeley-Illinois-Maryland Association interferometer. The HCN observations comprise the first high-resolution (θ ~ 5''-10'') survey of dense molecular gas from a sample of normal galaxies, rather than galaxies with prolific starburst or nuclear activities. The images show compact structure, demonstrating that the dense gas emission is largely confined to the central kiloparsec of the sources. To within the uncertainties, 70%-100% of the single-dish flux is recovered for each source; this implies that there is not a significant contribution to the HCN flux from low-level emission in the disks of the galaxies. In one of the galaxies, NGC 6946, the ratio of HCN to CO integrated intensities ranges from 0.05-0.2 within the extent of the HCN emission (r = 150 pc), with an average value of 0.11 ± 0.01 over the whole region; the range and average values of the ratios in NGC 6946 are very similar to what is observed in the central r = 250 pc of the Milky Way. A comparison with single-dish observations allows us to place an upper limit of 0.01 on the ratio of integrated intensities in the region 150 < r < 800 pc in NGC 6946. In NGC 6946, NGC 1068 and the Milky Way, the ratio I_HCN/I_CO is 5-10 times higher in the bulge regions than in their disks; this suggests that the physical conditions in their bulges and disks are very different. Furthermore, the presence of dense gas on size scales of ~500 pc in the centers of these nearby galaxies and the Milky Way suggests that the internal pressure is at least 10⁷ cm^-3 K in their centers; this is some 3 orders of magnitude greater than the pressure in the local interstellar medium in the Milky Way, and it is 2 orders of magnitude greater than the pressure from the self-gravity of a solar neighborhood giant molecular cloud. In NGC 4826 and M51, as in the Milky Way and NGC 1068, there is a linear offset of ~100 pc between the dense gas distribution and the peak of the radio continuum emission. We did not detect HCN toward three additional spiral galaxies.