We present a comprehensive survey of boron abundances in diffuse interstellar clouds from observations made with the Space Telescope Imaging Spectrograph (STIS) of the Hubble Space Telescope. Our sample of 56 Galactic sight lines is the result of a complete search of archival STIS data for the BII{lambda}1362 resonance line, with each detection confirmed by the presence of absorption from OI{lambda}1355, CuII{lambda}1358, and GaII{lambda}1414 (when available) at the same velocity. Five previous measurements of interstellar BII from Goddard High Resolution Spectrograph (GHRS) observations are incorporated in our analysis, yielding a combined sample that more than quadruples the number of sight lines with significant boron detections. Our survey also constitutes the first extensive analysis of interstellar gallium from STIS spectra and expands on previously published results for oxygen and copper. The observations probe both high- and low-density diffuse environments, allowing the density-dependent effects of interstellar depletion to be clearly identified in the gas-phase abundance data for each element.