Visible Light Communications (VLC) has been studied thoroughly in recent years as an alternative or complementary technology to radio frequency communications. The reliability of VLC channels highly depends on the availability and alignment of line of sight links. In this work, we study the effect of random receiver orientation for mobile users over VLC downlink channels, which affects the existence of line of sight links and the receiver field of view. Based on the statistics of vertical receiver orientation and user mobility, we develop a unified analytical framework to characterize the statistical distribution of VLC downlink channels, which is then utilized to obtain the outage probability and the bit error rate. Our analysis is generalized for arbitrary distributions of receiver orientation/location for a single transmitter, and extended to multiple transmitter case for certain scenarios. Extensive Monte Carlo simulations show a perfect match between the analytical and the simulation data in terms of both the statistical channel distribution and the resulting bit error rate. Our results also characterize the channel attenuation due to random receiver orientation/location for various scenarios of interest.