  We present the first systematic investigation of the existence, spatial
distribution, and kinematics of warm ionized gas as traced by the [O II] 3727AA
emission line in 74 of the most massive galaxies in the local Universe. All of
our galaxies have deep integral field spectroscopy from the volume- and
magnitude-limited MASSIVE survey of early-type galaxies with stellar mass
log(M_*/M_sun) > 11.5 (M_K < -25.3 mag) and distance D < 108 Mpc. Of the 74
galaxies in our sample, we detect warm ionized gas in 28, which yields a global
detection fraction of 38\pm6% down to a typical [O II] equivalent width limit
of 2AA. MASSIVE fast rotators are more likely to have gas than MASSIVE slow
rotators with detection fractions of 80\pm10% and 28\pm6%, respectively. The
spatial extents span a wide range of radii (0.6 - 18.2 kpc; 0.1 - 4R_e), and
the gas morphologies are diverse, with 17/28 = 61\pm9% being centrally
concentrated, 8/28 = 29\pm9% exhibiting clear rotation out to several kpc, and
3/28 = 11\pm6% being extended but patchy. Three out of four fast rotators show
kinematic alignment between the stars and gas, whereas the two slow rotators
with robust kinematic measurements available exhibit kinematic misalignment.
Our inferred warm ionized gas masses are roughly ~10^5M_sun. The emission line
ratios and radial equivalent width profiles are generally consistent with
excitation of the gas by the old underlying stellar population. We explore
different gas origin scenarios for MASSIVE galaxies and find that a variety of
physical processes are likely at play, including internal gas recycling,
cooling out of the hot gaseous halo, and gas acquired via mergers.
