Most successful galaxy formation scenarios now postulate that the intense star formation in massive, high-redshift galaxies during their major growth period was truncated when powerful AGNs launched galaxy-wide outflows of gas that removed large parts of the interstellar medium. SINFONI imaging spectroscopy of the most powerful radio galaxies at z ∼ 2 show clear signatures of such winds, but are too rare to be good representatives of a generic phase in the evolution of all massive galaxies at high redshift. Here we present SINFONI imaging spectroscopy of the rest-frame optical emission-line gas in 12 radio galaxies at redshifts ∼2. Our sample spans a range in radio power that is intermediate between the most powerful radio galaxies with known wind signatures at these redshifts and vigorous starburst galaxies, and are about two orders of magnitude more common than the most powerful radio galaxies. Thus, if AGN feedback is a generic phase of massive galaxy evolution for reasonable values of the AGN duty cycle, these are just the sources where AGN feedback should be most important. Our sources show a diverse set of gas kinematics ranging from regular velocity gradients with amplitudes of Δv = 200−400 km s −1 consistent with rotating disks to very irregular kinematics with multiple velocity jumps of a few 100 km s −1 . Line widths are generally high, typically around FWHM = 800 km s −1 , more similar to the more powerful high-z radio galaxies than mass-selected samples of massive high-z galaxies without bright AGNs, and consistent with the velocity range expected from recent hydrodynamic models. A broad Hα line in one target implies a black hole mass of a few 10 9 M . Velocity offsets of putative satellite galaxies near a few targets suggest dynamical masses of a few 10 11 M for our sources, akin to the most powerful high-z radio galaxies. Ionized gas masses are 1−2 orders of magnitude lower than in the most powerful radio galaxies, and the extinction in the gas is relatively low, up to A V ∼ 2 mag. The ratio of line widths, σ, to bulk velocity, v, is so large that even the gas in galaxies with regular velocity fields is unlikely to be gravitationally bound. It is unclear, however, whether the large line widths are due to turbulence or unresolved, local outflows as are sometimes observed at low redshifts. We compare our sources with sets of radio galaxies at low and high redshift, finding that they may have more in common with gas-rich nearby radio galaxies with similar jet power than with the most powerful high-z radio galaxies. Comparison of the kinetic energy with the energy supply from the AGNs through jet and radiation pressure suggests that the radio source still plays a dominant role for feedback, consistent with low-redshift radio-loud quasars.