We present optical longslit spectroscopic observations of 21 low-luminosity, extreme late-type spiral galaxies. Our sample is comprised of Sc-Sm Local Supercluster spirals with moderate-to-low optical surface brightnesses and with luminosities at the low end for spiral disk galaxies (M_V>-18.8). For each galaxy we have measured high spatial resolution position-velocity (P-V) curves using the H alpha emission line, and for 15 of the galaxies we also derive major axis rotation curves. In ~50% of our sample, the P-V curves show significant asymmetries in shape, extent, and/or amplitude on the approaching and receding sides of the disk. A number of the P-V curves are still rising to the last measured point, or reach a clear turnover on only one side. In most instances we find good agreement between the kinematic centers of extreme late-type spirals as defined by the global HI emission profile and by their optical continuum, although in a few cases we see evidence of possible real offsets. In spite of their shallow central gravitational potentials, at least 6 of the galaxies in our sample possess semi-stellar nuclei that appear to be compact nuclear star clusters; in 5 of these cases we see kinematic signatures in the P-V curves at the location of the nucleus. Finally, we find that like giant spirals, our sample galaxies have higher specific angular momenta than predicted by current cold dark matter models.