We explore the effects of nuclear masses on the temperature and neutron density conditions required for r-process nucleosynthesis using four nuclear mass models augmented by the latest atomic mass evaluation. For each model we derive the conditions for producing the observed abundance peaks at mass numbers A ∼ 80, 130, and 195 under the waiting-point approximation and further determine the sets of conditions that can best reproduce the r-process abundance patterns (r-patterns) inferred for the solar system and observed in metal-poor stars of the Milky Way halo. In broad agreement with previous studies, we find that (1) the conditions for producing abundance peaks at A ∼ 80 and 195 tend to be very different, which suggests that at least for some nuclear mass models, these two peaks are not produced simultaneously; (2) the typical conditions required by the critical waiting-point (CWP) nuclei with the N = 126 closed neutron shell overlap significantly with those required by the N = 82 CWP nuclei, which enables coproduction of abundance peaks at A ∼ 130 and 195 in accordance with observations of many metal-poor stars; and (3) the typical conditions required by the N = 82 CWP nuclei can reproduce the r-pattern observed in the metal-poor star HD 122563, which differs greatly from the solar r-pattern. We also examine how nuclear mass uncertainties affect the conditions required for the r-process and identify some key nuclei including 76 Ni to 78 Ni, 82 Zn, 131 Cd, and 132 Cd for precise mass measurements at rare-isotope beam facilities.