We relate transitions in galaxy structure and gas content to refueling, here defined to include both the external gas accretion and the internal gas processing needed to renew reservoirs for star formation. We analyze two z=0 data sets: a high-quality ~200 galaxy sample (the Nearby Field Galaxy Survey, data release herein) and a volume-limited ~3000 galaxy sample with reprocessed archival data. Both reach down to baryonic masses ~10^9^M_{sun}_ and span void-to-cluster environments. Two mass-dependent transitions are evident: (1) below the "gas-richness threshold" scale (V~125km/s), gas-dominated quasi-bulgeless Sd-Im galaxies become numerically dominant; while (2) above the "bimodality" scale (V~200km/s), gas-starved E/S0s become the norm. Notwithstanding these transitions, galaxy mass (or V as its proxy) is a poor predictor of gas-to-stellar mass ratio M_gas_/M_*_. Instead, M_gas_/M_*_ correlates well with the ratio of a galaxy's stellar mass formed in the last Gyr to its preexisting stellar mass, such that the two ratios have numerically similar values. This striking correspondence between past-averaged star formation and current gas richness implies routine refueling of star-forming galaxies on Gyr timescales. We argue that this refueling underlies the tight M_gas_/M_*_ versus color correlations often used to measure "photometric gas fractions." Furthermore, the threshold and bimodality scale transitions reflect mass-dependent demographic shifts between three refueling regimes--accretion-dominated, processing-dominated, and quenched. In this picture, gas-dominated dwarfs are explained not by inefficient star formation but by overwhelming gas accretion, which fuels stellar mass doubling in <~1Gyr. Moreover, moderately gas-rich bulged disks such as the Milky Way are transitional, becoming abundant only in the narrow range between the threshold and bimodality scales.