We use cosmological simulations from the FIRE (Feedback In Realistic Environments) project to study the baryon cycle and galaxy mass assembly for central galaxies in the halo mass range $M_{rm halo} sim 10^{10} - 10^{13} M_{odot}$. By tracing cosmic inflows, galactic outflows, gas recycling, and merger histories, we quantify the contribution of physically distinct sources of material to galaxy growth. We show that in situ star formation fueled by fresh accretion dominates the early growth of galaxies of all masses, while the re-accretion of gas previously ejected in galactic winds often dominates the gas supply for a large portion of every galaxys evolution. Externally processed material contributes increasingly to the growth of central galaxies at lower redshifts. This includes stars formed ex situ and gas delivered by mergers, as well as smooth intergalactic transfer of gas from other galaxies, an important but previously under-appreciated growth mode. By $z=0$, wind transfer, i.e. the exchange of gas between galaxies via winds, can dominate gas accretion onto $sim L^{*}$ galaxies over fresh accretion and standard wind recycling. Galaxies of all masses re-accrete >50% of the gas ejected in winds and recurrent recycling is common. The total mass deposited in the intergalactic medium per unit stellar mass formed increases in lower mass galaxies. Re-accretion of wind ejecta occurs over a broad range of timescales, with median recycling times ($sim 100-350$ Myr) shorter than previously found. Wind recycling typically occurs at the scale radius of the halo, independent of halo mass and redshift, suggesting a characteristic recycling zone around galaxies that scales with the size of the inner halo and the galaxys stellar component.
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