We present two large catalogs of active galactic nucleus (AGN) candidates identified across 30,093 deg2 of extragalactic sky from the Wide-field Infrared Survey Explorer's AllWISE Data Release. Both catalogs are selected purely using the Wide-field Infrared Survey Explorer (WISE) W1 and W2 bands. The R90 catalog consists of 4,543,530 AGN candidates with 90% reliability, while the C75 catalog consists of 20,907,127 AGN candidates with 75% completeness. These reliability and completeness figures were determined from a detailed analysis of UV- to near-IR spectral energy distributions of sources in the 9 deg2 Boötes field. The AGN selection criteria are based on those of Assef et al. (2013) recalibrated to the AllWISE data release. We provide a detailed discussion of potential artifacts and excise portions of the sky close to the Galactic Center, Galactic Plane, nearby galaxies, and other expected contaminating sources. These catalogs are expected to enable a broad range of science, and we present a few illustrative cases. From the R90 sample, we identify 45 highly variable AGNs lacking radio counterparts in the FIRST survey. One of these sources, WISEA J142846.71+172353.1, is a changing-look quasar at z = 0.104, which has changed from having broad H to being a narrow-lined AGN. We characterize our catalogs by comparing them to large, wide-area AGN catalogs in the literature. We identify four ROSAT X-ray sources that are each matched to three WISE-selected AGNs in the R90 sample within 30″. Spectroscopy reveals that one of these systems, 2RXS J150158.6+691029, consists of a triplet of quasars at z = 1.133 0.004, suggestive of a rich group or forming galaxy cluster.