We present the HI content of galaxies in nearby groups and clusters as measured by the 70% complete Arecibo Legacy Fast-ALFA (ALFALFA) survey, including constraints from ALFALFA detection limits. Our sample includes 22 systems at distances between 70-160 Mpc over the mass range 12.5<log M/M_sun<15.0, for a total of 1986 late-type galaxies. We find that late-type galaxies in the centers of groups lack HI at fixed stellar mass relative to the regions surrounding them. Larger groups show evidence of a stronger dependence of HI properties on environment, despite a similar dependence of color on environment at fixed stellar mass. We compare several environment variables to determine which is the best predictor of galaxy properties; group-centric distance r and r/R_200 are similarly effective predictors, while local density is slightly more effective and group size and halo mass are slightly less effective. While both central and satellite galaxies in the blue cloud exhibit a significant dependence of HI content on local density, only centrals show a strong dependence on stellar mass, and only satellites show a strong dependence on halo mass. Finally, we see evidence that HI is deficient for blue cloud galaxies in denser environments even when both stellar mass and color are fixed. This is consistent with a picture where HI is removed or destroyed, followed by reddening within the blue cloud. Our results support the existence of pre-processing in isolated groups, along with an additional rapid mechanism for gas removal within larger groups and clusters, perhaps ram-pressure stripping.