In the natural world, the brain must handle inherent delays in visual processing. This is particularly problematic in tasks such as intercepting rapidly moving objects.  One compensatory strategy is to use prior experience together with current sensory data to predict future visual state, so that actions can be planned ahead of time. However the role of such prediction in controlling interceptive movements is not well established. There is substantial evidence for prediction in the control of eye movements, although the basis for such prediction and its potential role in interception are unclear. We have developed a virtual racquetball environment and have examined predictive saccades while intercepting balls. We find that predictive saccades are a pervasive aspect of performance. Subjects target a point on the trajectory of the ball, where it will pass subsequent to a bounce, with high accuracy, and compensate for variations in trajectory, velocity, and elasticity. This suggests that subjects use learnt knowledge of ball dynamics to predict where the ball will be after the bounce, and when it will get there. The complexity of the prediction rules out simple models such as visual interpolation or extrapolation. Instead, elasticity, 3D velocity, and gravity all are likely to be taken into account. Since eye, head, arm, and body movements all co-occur, it seems likely that a common internal model for predicting visual state is shared by different effectors to coordinate interceptive movements.