Binary microlensing light curves have a variety of morphologies. Many are indistinguishable from point-lens light curves. Of those that deviate from the point-lens form, caustic crossing light curves have tended to dominate identified binary-lens events. Other distinctive signatures of binary lenses include significant asymmetry, multiple peaks, and repeating events. We have quantified, using high-resolution simulations, the theoretically expected relative numbers of each type of binary-lens event, based on its measurable characteristics. We find that a microlensing survey with current levels of photometric uncertainty and sampling should contain at least as many non-caustic crossing binary-lens events as caustic crossing events; in future surveys with more sensitive photometry, the contribution of distinctive non-caustic crossing events will be even greater. To show that this result is robust, we investigate the influence of several physical effects, including blending, sampling rate, and various binary populations.