We have performed an absorption-line survey of outflowing gas in 78 starburst-dominated, infrared-luminous galaxies. This is the largest study of superwinds at z < 3. Superwinds are found in almost all infrared-luminous galaxies, and changes in detection rate with SFR--winds are found twice as often in ultraluminous infrared galaxies (ULIRGs) as in less-luminous galaxies--reflect different wind geometries. The maximum velocities we measure are 600 km/s, though most of the outflowing gas has lower velocities (100-200 km/s). (One galaxy has velocities exceeding 1000 km/s.) Velocities in LINERs are higher than in HII galaxies, and outflowing ionized gas often has higher velocities than the neutral gas. Wind properties (velocity, mass, momentum, and energy) scale with galaxy properties (SFR, luminosity, and galaxy mass), consistent with ram-pressure driving of the wind. Wind properties increase strongly with increasing galactic mass, contrary to expectation. These correlations flatten at high SFR (> 10-100 M_sun/yr), luminosities, and masses. This saturation is due to a lack of gas remaining in the wind's path, a common neutral gas terminal velocity, and/or a decrease in the efficiency of thermalization of the supernovae energy. It means that mass entrainment efficiency, rather than remaining constant, declines in galaxies with SFR > 10 M_sun/yr and M_K < -24. Half of our sample consists of ULIRGs, which host as much as half of the star formation in the universe at z > 1. The powerful, ubiquitous winds we observe in these galaxies imply that superwinds in massive galaxies at redshifts above unity play an important role in the evolution of galaxies and the intergalactic medium.