We present EMPIRE, an IRAM 30-m large program that mapped $lambda = 3{-}4$ mm dense gas tracers at $sim 1{-}2,$kpc resolution across the whole star-forming disk of nine nearby, massive, spiral galaxies. We describe the EMPIRE observing and reduction strategies and show new whole-galaxy maps of HCN(1-0), HCO$^+$(1-0), HNC(1-0) and CO(1-0). We explore how the HCN-to-CO and IR-to-HCN ratios, observational proxies for the dense gas fraction and dense gas star formation efficiency, depend on host galaxy and local environment. We find that the fraction of dense gas correlates with stellar surface density, gas surface density, molecular-to-atomic gas ratio, and dynamical equilibrium pressure. In EMPIRE, the star formation rate per unit dense gas anti-correlates with these same environmental parameters. Thus, although dense gas appears abundant the central regions of many spiral galaxies, this gas appears relatively inefficient at forming stars. These results qualitatively agree with previous work on nearby galaxies and the Milky Ways Central Molecular Zone. To first order, EMPIRE demonstrates that the conditions in a galaxy disk set the gas density distribution and that the dense gas traced by HCN shows an environment-dependent relation to star formation. However, our results also show significant ($pm 0.2$ dex) galaxy-to-galaxy variations. We suggest that gas structure below the scale of our observations and dynamical effects likely also play an important role.
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