We report the detection of ubiquitous powerful nuclear outflows in massive (> or =, slanted10 super(11) M sub(middot in circle)) z ~ 2 star-forming galaxies (SFGs), which are plausibly driven by an active galactic nucleus (AGN). The sample consists of the eight most massive SFGs from our SINS/zC-SINF survey of galaxy kinematics with the imaging spectrometer SINFONI, six of which have sensitive high-resolution adaptive optics-assisted observations. All of the objects are disks hosting a significant stellar bulge. The spectra in their central regions exhibit a broad component in Halpha and forbidden NII and SII line emission, with typical velocity FWHM ~ 1500 km s super(-1), NII/Halpha ratio approximately 0.6, and intrinsic extent of 2-3 kpc. These properties are consistent with warm ionized gas outflows associated with Type 2 AGN, the presence of which is confirmed via independent diagnostics in half the galaxies. The data imply a median ionized gas mass outflow rate of ~60M yr super(-1) and mass loading of ~3. At larger radii, a weaker broad component is detected but with lower FWHM ~485 km s super(-1) and NII/Halpha approximately 0.35, characteristic for star formation-driven outflows as found in the lower-mass SINS/zC-SINF galaxies. The high inferred mass outflow rates and frequent occurrence suggest that the nuclear outflows efficiently expel gas out of the centers of the galaxies with high duty cycles and may thus contribute to the process of star formation quenching in massive galaxies. Larger samples at high masses will be crucial in confirming the importance and energetics of the nuclear outflow phenomenon and its connection to AGN activity and bulge growth.