We measure the low-J CO line ratios R_21_=CO(2-1)/CO(1-0), R_32_=CO(3-2)/CO(2-1), and R_31_=CO(3-2)/CO(1-0) using whole-disk CO maps of nearby galaxies. We draw CO(2-1) from PHANGS-ALMA, HERACLES, and follow-up IRAM surveys; CO(1-0) from COMING and the Nobeyama CO Atlas of Nearby Spiral Galaxies; and CO(3-2) from the James Clerk Maxwell Telescope Nearby Galaxy Legacy Survey and Atacama Pathfinder Experiment Large APEX Sub-Millimetre Array mapping. All together, this yields 76, 47, and 29 maps of R_21_, R_32_, and R_31_ at 20"~1.3kpc resolution, covering 43, 34, and 20 galaxies. Disk galaxies with high stellar mass, log(M_*_/M_{sun}_)=10.25--11, and star formation rate (SFR)=1-5M_{sun}_/yr, dominate the sample. We find galaxy-integrated mean values and a 16%-84% range of R_21_=0.65(0.50-0.83), R_32_=0.50(0.23-0.59), and R_31_=0.31(0.20-0.42). We identify weak trends relating galaxy-integrated line ratios to properties expected to correlate with excitation, including SFR/M_*_ and SFR/L_CO_. Within galaxies, we measure central enhancements with respect to the galaxy-averaged value of ~0.18_-0.14_^+0.09^dex for R_21_, 0.27_-0.15_^+0.13^dex for R_31_, and 0.08_-0.09_^+0.11^dex for R32. All three line ratios anticorrelate with galactocentric radius and positively correlate with the local SFR surface density and specific SFR, and we provide approximate fits to these relations. The observed ratios can be reasonably reproduced by models with low temperature, moderate opacity, and moderate densities, in good agreement with expectations for the cold interstellar medium. Because the line ratios are expected to anticorrelate with the CO(1-0)-to-H2 conversion factor, {alpha}_CO_^1-0^, these results have general implications for the interpretation of CO emission from galaxies.