The angular distribution of stars brighter than visual magnitude 14 is analyzed for evidence of gravitationally bound systems with widely separated components. Binary stars with separations on the order of 0.1 parsec are interesting as probes of Galactic dynamics, disk dark matter, the Oort comet cloud, and the postulated solar companion star, Nemesis. Catalogs of stars, complete to a resolution limit of four arcseconds, were constructed from digitized Schmidt telescope plates covering over 600 square degrees of the sky in four directions. I analyze the clustering properties of stars and star pairs using two-point and three-point angular correlation functions. Significant correlation (assumed to be due to binary stars) is detected only for angular separations less than 40 arcseconds. No significant numbers of ternary systems are detected. Employing a modified Wasserman-Weinberg technique, I directly compare the angular correlation functions with a simple model of wide binary star properties. The wide binary semimajor axis distribution at low Galactic latitudes is best described as a single power law of index -1.3. Near the North Galactic Pole (NGP), the power law is less steep and the distribution is consistent with a cutoff near 0.1~parsec. The derived wide binary density is unrealistically large, suggesting that the basic model inadequately characterizes wide binary properties. I also study a sample of stars from the Space Telescope Guide Star Catalog (GSC). The region analyzed lies within thirty degrees of the NGP and covers 2500 square degrees of sky. This large, low-resolution sample complements the smaller, more uniform plate catalogs. I identify many systematic errors in the GSC and attempt to account for image misclassifications and poorly defined resolution limits. The corrected stellar correlation function from the GSC is found to be consistent with a wide binary separation cutoff near 0.1parsec. The dissolution of a poor Galactic cluster at the NGP may explain the observed wide binary distribution in that direction. Evidence for weak clustering on scales of one degree is seen in the pair-pair correlation function. The unphysically large wide binary density derived from magnitude-limited samples is explained well by a luminosity correlation between the binary components. An alternative solution requires all F to K dwarfs to be members of wide binaries. Based on the observed properties of wide binary stars, the probability that the Sun has a stellar companion capable of inducing periodic mass extinctions on Earth is only 0.05 percent. In an analogy with Oort cloud dynamics, I suggest a mechanism that can substantially reduce the number of wide binaries with separations greater than 0.1 parsec.