The Robo-AO Kepler Planetary Candidate Survey is observing every Kepler planet candidate host star with laser adaptive optics imaging to search for blended nearby stars, which may be physically associated companions and/or responsible for transit false positives. In this paper, we present the results of our search for stars nearby 1629 Kepler planet candidate hosts. With survey sensitivity to objects as close as ~0.15", and magnitude differences {Delta}m=<6, we find 223 stars in the vicinity of 206 target KOIs; 209 of these nearby stars have not been previously imaged in high resolution. We measure an overall nearby-star probability for Kepler planet candidates of 12.6%+/-0.9% at separations between 0.15" and 4.0". Particularly interesting KOI systems are discussed, including 26 stars with detected companions that host rocky, habitable zone candidates and five new candidate planet-hosting quadruple star systems. We explore the broad correlations between planetary systems and stellar binarity, using the combined data set of Baranec et al. (2016, J/AJ/152/18) and this paper. Our previous 2{sigma} result of a low detected nearby star fraction of KOIs hosting close-in giant planets is less apparent in this larger data set. We also find a significant correlation between detected nearby star fraction and KOI number, suggesting possible variation between early and late Kepler data releases.