The line-of-sight velocity distributions (LOSVDs) have been measured to > R_e_/2 along the major axes of 44 elliptical galaxies (more than 80 per cent of all ellipticals north of δ = -10^deg^ and brighter than B_T_ = 12.0), together with stellar rotational velocity and velocity dispersion profiles. For 19 of these 44 objects, minor axis profiles are also given. Monte Carlo simulations have been used to estimate errors. LOSVDs are found to deviate from Gaussians by no more than ~10 per cent. If rotation is present, LOSVDs are asymmetric with the prograde wings being always steeper than the retrograde wings. The degree of asymmetry (measured by the H_3_ Gauss-Hermite coefficient) correlates with ν/σ. Round and boxy ellipticals have lower asymmetries than flat and discy ones. On the whole, both types must have intrinsically asymmetric velocity distributions. Symmetric deviations (measured by the H_4_ Gauss-Hermite coefficient) are generally smaller than asymmetric ones. On the basis of the observed LOSVD shapes, the validity of two- integral models can be ruled out for most of the non-discy objects observed here (discy ellipticals require detailed modelling before similar conclusions can be drawn). Discy ellipticals have H_3_ and H_4_ major and minor axis profiles which appear consistent with a bulge+disc superposition. The observed H_4_ profile in M87 argues for radially anisotropic spherical or oblate models. Velocity dispersion profiles show significant individuality, but typically become flat outside R_e_/4. Major and minor axis slopes are mostly correlated one to one. We confirm that, with increasing luminosity, ellipticals become more anisotropic and that discy ellipticals have more rotational support. The Fundamental Plane of elliptical galaxies is tighter if total kinetic energy is used instead of central velocity dispersion. Both the small scatter about the Fundamental Plane and the homogenous and systematic properties of the LOSVDs imply that only a small range of dynamical models is realized in elliptical galaxies.