We report the results of a Sloan Digital Sky Survey IV eBOSS program to target X-ray sources and mid-infrared-selected Wide-field Infrared Survey Explorer (WISE) active galactic nucleus (AGN) candidates in a 36.8deg^2^ region of Stripe 82. About half this survey (15.6deg^2^) covers the largest contiguous portion of the Stripe 82 X-ray survey. This program represents the largest spectroscopic survey of AGN candidates selected solely by their WISE colors. We combine this sample with X-ray and WISE AGNs in the field identified via other sources of spectroscopy, producing a catalog of 4847 sources that is 82% complete to r~22. Based on X-ray luminosities or WISE colors, 4730 of these sources are AGNs, with a median sample redshift of z~1. About 30% of the AGNs are optically obscured (i.e., lack broad lines in their optical spectra). BPT analysis, however, indicates that 50% of the WISE AGNs at z<0.5 have emission line ratios consistent with star-forming galaxies, so whether they are buried AGNs or star-forming galaxy contaminants is currently unclear. We find that 61% of X-ray AGNs are not selected as mid-infrared AGNs, with 22% of X-ray AGNs undetected by WISE. Most of these latter AGNs have high X-ray luminosities (Lx>10^44^erg/s), indicating that mid-infrared selection misses a sizable fraction of the highest luminosity AGNs, as well as lower luminosity sources where AGN-heated dust is not dominating the mid-infrared emission. Conversely, ~58% of WISE AGNs are undetected by X-rays, though we do not find that they are preferentially redder than the X-ray-detected WISE AGNs.