We present ionized-gas ([OIII]lambda 5007 angstrom) and stellar kinematics (velocities and velocity dispersions) for 30 nearly face-on spiral galaxies out to as many as three K-band disk scale lengths (h(R)). These data have been derived from PPak integral-field-unit spectroscopy from 4980-5370 angstrom observed at a mean resolution of lambda/Delta lambda = 7700 (sigma(inst) = 17 km s(-1)). These data are a fundamental product of our survey and will be used in companion papers to, e. g., derive the detailed (baryonic+dark) mass budget of each galaxy in our sample. Our presentation provides a comprehensive description of the observing strategy and data reduction, including a robust measurement and removal of shift, scale, and rotation effects in the data due to instrumental flexure. Using an in-plane coordinate system determined by fitting circular-speed curves to our velocity fields, we derive azimuthally averaged rotation curves and line-of-sight velocity dispersion (sigma(LOS)) and luminosity profiles for both the stars and [OIII]-emitting gas. Along with a clear presentation of the data, we demonstrate: (1) The [OIII] and stellar rotation curves exhibit a clear signature of asymmetric drift with a rotation difference that is 11% of the maximum rotation speed of the galaxy disk, comparable to measurements in the solar neighborhood in the Milky Way. (2) The e-folding length of the stellar velocity dispersion (h(sigma)) is 2h(R) on average, as expected for a disk with a constant scale height and mass-to-light ratio, with a scatter that is notably smaller for massive, high-surface-brightness disks in the most luminous galaxies. (3) At radii larger than 1.5h(R), sigma(LOS) tends to decline slower than the best-fitting exponential function, which may be due to an increase in the disk mass-to-light ratio, disk flaring, or disk heating by the dark-matter halo. (4) A strong correlation exists between the central vertical stellar velocity dispersion of the disks (sigma(z,0)) and their circular rotational speed at 2.2h(R) (V-2.2hR(OIII)), with a zero point indicating that galaxy disks are submaximal. Moreover, weak but consistent correlations exist between sigma(z,0)/V-2.2hR(OIII) and global galaxy properties such that disks with a fainter central surface brightness in bluer and less luminous galaxies of later morphological types are kinematically colder with respect to their rotational velocities.