We present results of a comprehensive infrared coronagraphic search for substellar companions to nearby stars. The research consisted of (1) a 178-star survey at Steward and Lick observatories, with optical follow-up from Keck Observatory, capable of detecting companions with masses greater than 30 M-J, and semimajor axes between about 140 to 1200 AU; (2) a 102-star survey using the Keck Telescope, capable of detecting extrasolar brown dwarfs and planets typically more massive than 10 M-J, with semimajor axes between about 75 and 300 AU. Only one brown dwarf companion was detected, and no planets. The frequency of brown dwarf companions to G, K, and M stars orbiting between 75 and 300 AU is measured to be 1%+/-1%, the most precise measurement of this quantity to date. The frequency of massive (greater than 30 M-J) brown dwarf companions at 120-1200 AU is found to be f=0.7%+/-0.7%. The frequency of giant planet companions with masses between 5 and 10 M-J orbiting between 75 and 300 AU is measured here for the first time to be no more than similar to3%. Together with other surveys that encompass a wide range of orbital separations, these results imply that substellar objects with masses between 12 and 75 M-J form only rarely as companions to stars. Theories of star formation that could explain these data are only now beginning to emerge.