We present the stellar kinematic maps of a large sample of galaxies from the integral-field spectroscopic survey CALIFA. The sample comprises 300 galaxies displaying a wide range of morphologies across the Hubble sequence, from ellipticals to late-type spirals. This dataset allows us to homogeneously extract stellar kinematics up to several effective radii. In this paper, we describe the level of completeness of this subset of galaxies with respect to the full CALIFA sample, as well as the virtues and limitations of the kinematic extraction compared to other well-known integral-field surveys. In addition, we provide averaged integrated velocity dispersion radial profiles for different galaxy types, which are particularly useful to apply aperture corrections for single aperture measurements or poorly resolved stellar kinematics of high-redshift sources. The work presented in this paper sets the basis for the study of more general properties of galaxies that will be explored in subsequent papers of the survey.