We quantify the presence of active galactic nuclei (AGNs) in a mass-complete (M > 5 × 10 M ) sample of 123 star-forming and quiescent galaxies at 1.5 = z = 2.5, using X-ray data from the 4 Ms Chandra Deep Field-South (CDF-S) survey. 41% ± 7% of the galaxies are detected directly in X-rays, 22% ± 5% with rest-frame 0.5-8 keV luminosities consistent with hosting luminous AGNs (L > 3 × 10 erg s ). The latter fraction is similar for star-forming and quiescent galaxies, and does not depend on galaxy stellar mass, suggesting that perhaps luminous AGNs are triggered by external effects such as mergers. We detect significant mean X-ray signals in stacked images for both the individually non-detected star-forming and quiescent galaxies, with spectra consistent with star formation only and/or a low-luminosity AGN in both cases. Comparing star formation rates inferred from the 2-10 keV luminosities to those from rest-frame IR+UV emission, we find evidence for an X-ray excess indicative of low-luminosity AGNs. Among the quiescent galaxies, the excess suggests that as many as 70%-100% of these contain low- or high-luminosity AGNs, while the corresponding fraction is lower among star-forming galaxies (43%-65%). Our discovery of the ubiquity of AGNs in massive, quiescent z ~ 2 galaxies provides observational support for the importance of AGNs in impeding star formation during galaxy evolution.