Emerging media technologies such as 3D film and head-mounted displays (HMDs) call for new types of spatial interaction. Here we describe and evaluate AnyOrbit: a novel orbital navigation technique that enables flexible and intuitive 3D spatial navigation in virtual environments (VEs). Unlike existing orbital methods, we exploit toroidal rather than spherical orbital surfaces, which allow independent control of orbital curvature in vertical and horizontal directions. This control enables intuitive and smooth orbital navigation between any desired orbital centers and between any vantage points within VEs. AnyOrbit leverages our proprioceptive sense of rotation to enable navigation in VEs without inconvenient external motion trackers. In user studies, we demonstrate that within a sports spectating context, the technique allows smooth shifts in perspective at a rate comparable to broadcast sport, is fast to learn, and is without excessive simulator sickness in most users. The technique is widely applicable to gaming, computer-aided-design (CAD), data visualisation, and telepresence.