We present results of a reconnaissance for stellar companions to all 131 radial velocity-detected candidate extrasolar planetary systems known as of 2005 July 1. Common proper-motion companions were investigated using the multiepoch STScI Digitized Sky Surveys and confirmed by matching the trigonometric parallax distances of the primaries to companion distances estimated photometrically. We also attempt to confirm or refute companions listed in the Washington Double Star Catalog, in the Catalogs of Nearby Stars Series by Gliese and Jahreiß, in Hipparcos results, and in Duquennoy & Mayor's radial velocity survey. Our findings indicate that a lower limit of 30 (23%) of the 131 exoplanet systems have stellar companions. We report new stellar companions to HD 38529 and HD 188015 and a new candidate companion to HD 169830. We confirm many previously reported stellar companions, including six stars in five systems, that are recognized for the first time as companions to exoplanet hosts. We have found evidence that 20 entries in the Washington Double Star Catalog are not gravitationally bound companions. At least three (HD 178911, 16 Cyg B, and HD 219449), and possibly five (including HD 41004 and HD 38529), of the exoplanet systems reside in triple-star systems. Three exoplanet systems (GJ 86, HD 41004, and γ Cep) have potentially close-in stellar companions, with planets at roughly Mercury-Mars distances from the host star and stellar companions at projected separations of ~20 AU, similar to the Sun-Uranus distance. Finally, two of the exoplanet systems contain white dwarf companions. This comprehensive assessment of exoplanet systems indicates that solar systems are found in a variety of stellar multiplicity environments-singles, binaries, and triples-and that planets survive the post-main-sequence evolution of companion stars.