The durations and trajectories of our saccadic eye movements are remarkably stereotyped. We have no voluntary control over these properties but they are determined by the movement amplitude and, to a smaller extent, also by the movement direction and initial eye orientation. Here we show that the stereotyped durations and trajectories are optimal for minimizing the variability in saccade endpoints that is caused by motor noise. The optimal duration can be understood from the nature of the motor noise, which is a combination of signal-dependent noise favoring long durations, and constant noise, which prefers short durations. The different durations of horizontal vs. vertical and of centripetal vs. centrifugal saccades, and the somewhat surprising properties of saccades in oblique directions are also accurately predicted by the principle of minimizing movement variability. The simple and sensible principle of minimizing the consequences of motor noise thus explains the full stereotypy of saccadic eye movements. This suggests that saccades are so stereotyped because that is the best strategy to minimize movement errors for an open-loop motor system.