We present the lightcurves of 21 gravitational microlensing events from the first six years of the MACHO Project gravitational microlensing survey which are likely examples of lensing by binary systems . These events were manually selected from a total sample of \sim 350 candidate microlensing events which were either detected by the MACHO Alert System or discovered through retrospective analyses of the MACHO database . At least 14 of these 21 events exhibit strong ( caustic ) features , and 4 of the events are well fit with lensing by large mass ratio ( brown dwarf or planetary ) systems , although these fits are not necessarily unique . The total binary event rate is roughly consistent with predictions based upon our knowledge of the properties of binary stars , but a precise comparison can not be made without a determination of our binary lens event detection efficiency . Towards the Galactic bulge , we find a ratio of caustic crossing to non-caustic crossing binary lensing events of 12:4 , excluding one event for which we present 2 fits . This suggests significant incompleteness in our ability to detect and characterize non-caustic crossing binary lensing . The distribution of mass ratios , N ( q ) , for these binary lenses appears relatively flat . We are also able to reliably measure source-face crossing times in 4 of the bulge caustic crossing events , and recover from them a distribution of lens proper motions , masses , and distances consistent with a population of Galactic bulge lenses at a distance of 7 \pm 1 { kpc } . This analysis yields 2 systems with companions of \sim 0.05 { M } _ { \odot } .