Using data from the MOSFIRE Deep Evolution Field (MOSDEF) survey, we present a census of active galactic nucleus (AGN)-driven ionized outflows in a sample of 159 AGNs at 1.4 ≤ z ≤ 3.8. The sample spans AGN bolometric luminosities of 1044-47 erg s-1 and includes both quiescent and star-forming galaxies extending across 3 orders of magnitude in stellar mass. We identify and characterize outflows from the Hβ, [O iii], H, and [N ii] emission line spectra. We detect outflows in 17% of the AGNs, seven times more often than in a mass-matched sample of inactive galaxies in MOSDEF. The outflows are fast and galaxy-wide, with velocities of ∼400-3500 km s-1 and spatial extents of 0.3-11.0 kpc. The incidence of outflows among AGNs is independent of the stellar mass of the host galaxy, with outflows detected in both star-forming and quiescent galaxies. This suggests that outflows exist across different phases in galaxy evolution. We investigate relations between outflow kinematic, spatial, and energetic properties and both AGN and host galaxy properties. Our results show that AGN-driven outflows are widespread in galaxies along the star-forming main sequence. The mass-loading factors of the outflows are typically 0.1-1 and increase with AGN luminosity, capable of exceeding unity at at LAGN≳ 1046 erg s-1. In these more luminous sources, the ionized outflow alone is likely sufficient to regulate star formation and, when combined with outflowing neutral and molecular gas, may be able to quench star formation in their host galaxies