We report radial velocities for 844 FGKM-type main sequence and subgiant stars and 45 K giants, most of which had either low-precision velocity measurements or none at all. These velocities differ from the standard stars of Udry et al. by 0.035 km/s (RMS) for the 26 FGK standard stars in common. The zero-point of our velocities differs from that of Udry et al.: (V_present - V_Udry) = +0.053 km/s. Thus these new velocities agree with the best known standard stars both in precision and zero-point, to well within 0.1 km/s. Nonetheless, both these velocities and the standards suffer from three sources of systematic error, namely, convective blueshift, gravitational redshift, and spectral type mismatch of the reference spectrum. These systematic errors are here forced to be zero for G2V stars by using the Sun as reference, with Vesta and day sky as proxies. But for spectral types departing from solar, the systematic errors reach 0.3 km/s in the F and K stars and 0.4 km/s in M dwarfs. Multiple spectra were obtained for all 889 stars during four years, and 782 of them exhibit velocity scatter less than 0.1 km/s. These stars may serve as radial velocity standards if they remain constant in velocity. We found 11 new spectroscopic binaries and report orbital parameters for them.

76 pages, 23 figures, 4 tables, uses aastex.sty