We have conducted a high-resolution imaging study of the Taurus-Auriga star-forming region in order to characterize the primordial outcome of multiple star formation and the extent of the brown dwarf desert. Our survey identified 16 new binary companions to primary stars with masses of 0.25-2.5 M , raising the total number of binary pairs (including components of high-order multiples) with separations of 3-5000 AU to 90. We find that ~2/3-3/4 of all Taurus members are multiple systems of two or more stars, while the other ~1/4-1/3 appear to have formed as single stars; the distribution of high-order multiplicity suggests that fragmentation into a wide binary has no impact on the subsequent probability that either component will fragment again. The separation distribution for solar-type stars (0.7-2.5 M ) is nearly log-flat over separations of 3-5000 AU, but lower-mass stars (0.25-0.7 M ) show a paucity of binary companions with separations of 200 AU. Across this full mass range, companion masses are well described with a linear-flat function; all system mass ratios (q = MB /MA ) are equally probable, apparently including substellar companions. Our results are broadly consistent with the two expected modes of binary formation (free-fall fragmentation on large scales and disk fragmentation on small scales), but the distributions provide some clues as to the epochs at which the companions are likely to form.