In order to study the relationship between the gravitational potential and the properties of active galaxies, we have measured nuclear stellar and gaseous kinematics for a large sample of Seyfert galaxies. In this paper we present moderate-resolution data (80-230 km s(-1) EWHM) from two spectral regions, one in the near-infrared containing the Ca II triplet absorption features at similar to 8550 Angstrom and the [S III] 9069 Angstrom emission line, and the other in the visual including the Mg b absorption lines at similar to 5175 Angstrom and the [O III] 5007 Angstrom emission line. Nuclear stellar velocities, V*, and velocity dispersions, sigma*, were measured using the cross-correlation method. Complications for the kinematic analysis associated with the featureless continua and strong emission lines in Seyfert galaxies are briefly discussed. Emission-line velocities and widths were also measured from our spectra. The final sample contains 85 objects (22 type 1 Seyfert galaxies, 51 type 2 Seyferts, nine LINERs, and three normal galaxies). We provide a supplement to the database of narrow-line region and host galaxy properties compiled by Whittle (1992a) for 20 Seyfert galaxies not originally included. We plan to use our measurements in conjunction with this database to investigate the relationship between the nuclear gravitational potential and other properties of Seyfert galaxies.