Allowing viewers to explore virtual reality in a head-mounted display with six degrees of freedom (6-DoF) greatly enhances the associated immersion and comfort. It makes the experience more compelling compared to a fixed-viewpoint 2-DoF rendering produced by conventional algorithms using data from a stationary camera rig. In this work, we use subjective testing to study the relative importance of, and the interaction between, motion parallax and binocular disparity as depth cues that shape the perception of 3D environments by human viewers. Additionally, we use the recorded head trajectories to estimate the distribution of the head movements of a sedentary viewer exploring a virtual environment with 6-DoF. Finally, we demonstrate a real-time virtual reality rendering system that uses a Stacked OmniStereo intermediary representation to provide a 6-DoF viewing experience by utilizing data from a stationary camera rig. We outline the challenges involved in developing such a system and discuss the limitations of our approach.