We present results of the largest, most comprehensive study ever done of the stellar multiplicity of the most common stars in the Galaxy, the red dwarfs. We have conducted an all-sky volume-limited survey for stellar companions to 1120 M dwarf primaries known to lie within 25 pc of the Sun via trigonometric parallaxes. In addition to a comprehensive literature search, stars were explored in new surveys for companions at separations of 2″–300″. A reconnaissance of wide companions to separations of 300″ was done via blinking archival images. I-band images were used to search our sample for companions at separations of 2″–180″. Various astrometric and photometric methods were used to probe the inner 2″ to reveal close companions. We report the discovery of 20 new companions and identify 56 candidate multiple systems. We find a stellar multiplicity rate of 26.8 ± 1.4% and a stellar companion rate of 32.4 ± 1.4% for M dwarfs. There is a broad peak in the separation distribution of the companions at 4–20 au, with a weak trend of smaller projected linear separations for lower mass primaries. A hint that M-dwarf multiplicity may be a function of tangential velocity is found, with faster moving, presumably older, stars found to be multiple somewhat less often. We calculate that stellar companions make up at least 17% of mass attributed to M dwarfs in the solar neighborhood, with roughly 11% of M-dwarf mass hidden as unresolved companions. Finally, when considering all M-dwarf primaries and companions, we find that the mass distribution for M dwarfs increases to the end of the stellar main sequence.