We investigate the origin of the regularity and synchrony which have been observed in numerical experiments of two realistic models of molecular motors, namely Fisher-Kolomeisky's model of myosin V for vesicle transport in cells and Duke's model of myosin II for sarcomere shortening in muscle contraction. We show that there is a generic organizing principle behind the emergence of regular gait for a motor pulling a large cargo and synchrony of action of many motors pulling a single cargo. These results are surprising in that the models used are inherently stochastic, and yet they display regular behaviors in the parameter range relevant to experiments. Our results also show that these behaviors are not tied to the particular models used in these experiments, but rather are generic to a wide class of motor protein models.