We present spatially resolved two-dimensional stellar kinematics for the 41 most massive early-type galaxies (ETGs; M K –25.7 mag, stellar mass M * 10 11.8 M ) of the volume-limited ( D 〈 108 Mpc) MASSIVE survey. For each galaxy, we obtain high-quality spectra in the wavelength range of 3650–5850 Å from the 246-fibre Mitchell integral-field spectrograph at McDonald Observatory, covering a 107 arcsec x 107 arcsec field of view (often reaching 2 to 3 effective radii). We measure the 2D spatial distribution of each galaxy's angular momentum ( and fast or slow rotator status), velocity dispersion (), and higher order non-Gaussian velocity features (Gauss–Hermite moments h 3 to h 6 ). Our sample contains a high fraction (~80 per cent) of slow and non-rotators with 0.2. When combined with the lower mass ETGs in the ATLAS 3D survey, we find the fraction of slow rotators to increase dramatically with galaxy mass, reaching ~50 per cent at M K ~ –25.5 mag and ~90 per cent at M K –26 mag. All of our fast rotators show a clear anticorrelation between h 3 and V /, and the slope of the anticorrelation is steeper in more round galaxies. The radial profiles of show a clear luminosity and environmental dependence: the 12 most luminous galaxies in our sample ( M K –26 mag) are all brightest cluster/group galaxies (except NGC 4874) and all have rising or nearly flat profiles, whereas five of the seven ‘isolated’ galaxies are all fainter than M K = –25.8 mag and have falling . All of our galaxies have positive average h 4 ; the most luminous galaxies have average h 4 ~ 0.05, while less luminous galaxies have a range of values between 0 and 0.05. Most of our galaxies show positive radial gradients in h 4 , and those galaxies also tend to have rising profiles. We discuss the implications for the relationship among dynamical mass, , h 4 , and velocity anisotropy for these massive galaxies.