Human eye movements are stereotyped and repeatable, but how specific to a normal individual are the quantitative properties of his or her eye movements? We recorded saccades, anti-saccades and smooth-pursuit eye movements in a sample of over 1000 healthy young adults. A randomly selected subsample (10%) of participants were re-tested on a second occasion after a median interval of 18.8 days, allowing us to estimate reliabilities. Each of several derived measures, including latencies, accuracies, velocities, and left-right asymmetries, proved to be very reliable. We give normative means and distributions for each measure and describe the pattern of correlations amongst them. We identify several measures that exhibit significant sex differences. The profile of our oculomotor measures for an individual constitutes a personal oculomotor signature that distinguishes that individual from most other members of the sample of 1000.