In highly dynamic tasks that involve moving targets, planning is necessary to figure out when, where and how to intercept the target. In robotic table tennis in particular, motion planning can be very challenging due to time constraints, dimension of the search space and joint limits. Conventional planning algorithms often rely on a fixed virtual hitting plane to construct robot striking trajectories. These algorithms, however, generate restrictive strokes and can result in unnatural strategies when compared with human playing. In this paper, we introduce a new trajectory generation framework for robotic table tennis that does not involve a fixed hitting plane. A free-time optimal control approach is used to derive two different trajectory optimizers. The resulting two algorithms, Focused Player and Defensive Player, encode two different play-styles. We evaluate their performance in simulation and in our robot table tennis platform with a high speed cable-driven seven DOF robot arm. The algorithms return the balls with a higher probability to the opponent’s court when compared with a virtual hitting plane based method. Moreover, both can be run online and the trajectories can be corrected with new ball observations.