We examine the global H I properties of galaxies in quarter billion particle cosmological simulations using GADGET-2, focusing on how galactic outflows impact H I 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 (σ < 75 km s−1). To obtain predicted H I 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 H I mass function whose faint-end slope of −1.3 agrees well with observations from the Arecibo Fast Legacy ALFA survey; other models agree less well. Satellite galaxies have a bimodal distribution in H I fraction versus halo mass, with smaller satellites and/or those in larger haloes more often being H I deficient. At a given stellar mass, H I content correlates with the star formation rate and inversely correlates with metallicity, as expected if driven by stochasticity in the accretion rate. To higher redshifts, massive H I galaxies disappear and the mass function steepens. The global cosmic H I density conspires to remain fairly constant from z ∼ 5 → 0, but the relative contribution from smaller galaxies increases with redshift.