We examine the global HI properties of galaxies in quarter-billion particle cosmological simulations using Gadget-2, focusing on how galactic outflows impact HI content. We consider four outflow models, including a new one (ezw) motivated by recent interstellar medium simulations in which the wind speed and mass loading factor scale as expected for momentum-driven outflows for larger galaxies and energy-driven outflows for dwarfs (sigma<75 km/s). To obtain predicted HI masses, we employ a simple but effective local correction for particle self-shielding, and an observationally-constrained transition from neutral to molecular hydrogen. Our ezw simulation produces an HI mass function whose faint-end slope of -1.3 agrees well with observations from the ALFALFA survey; other models agree less well. Satellite galaxies have a bimodal distribution in HI fraction versus halo mass, with smaller satellites and/or those in larger halos more often being HI-deficient. At a given stellar mass, HI content correlates with star formation rate and inversely correlates with metallicity, as expected if driven by stochasticity in the accretion rate. To higher redshifts, massive HI galaxies disappear and the mass function steepens. The global cosmic HI density conspires to remain fairly constant from z~5-0, but the relative contribution from smaller galaxies increases with redshift.