We present results of a ground-based near-infrared campaign with Palomar TripleSpec, Keck NIRSPEC, and Gemini GNIRS to target two samples of reddened active galactic nucleus (AGN) candidates from the 31 deg(2) Stripe 82 X-ray survey. One sample, which is similar to 89% complete to K < 16 (Vega), consists of eight confirmed AGNs, four of which were identified with our follow-up program, and is selected to have red R - K colors (> 4, Vega). The fainter sample (K > 17, Vega) represents a pilot program to follow-up four sources from a parent sample of 34 that are not detected in the single-epoch SDSS catalog and have WISE quasar colors. All 12 sources are broad-line AGNs (at least one permitted emission line has an FWHM exceeding 1300 km s(-1)) and span a redshift range 0.59 < z < 2.5. Half the (R - K)-selected AGNs have features in their spectra suggestive of outflows. When comparing these sources to a matched sample of blue Type 1 AGNs, we find that the reddened AGNs are more distant (z > 0.5), and a greater percentage have high X-ray luminosities (L-X,L- full > 10(44) erg s(-1)). Such outflows and high luminosities may be consistent with the paradigm that reddened broad-line AGNs represent a transitory phase in AGN evolution as described by the major merger model for black hole growth. Results from our pilot program demonstrate proof of concept that our selection technique is successful in discovering reddened quasars at z > 1 missed by optical surveys.