In this paper, we consider a multi-input driftless bilinear system evolving on the n-dimensional sphere S-n. We first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on S-n. For the general framework, we establish the global controllability on S-n and propose two linear control laws on S-n that achieve asymptotic stabilization of an equilibrium point with an almost global domain-of-attraction. Further, the asymptotically stable closed-loop system trajectories are shown to be arcs on the geodesics of S-n for a particular choice of the equilibrium point. Next, we propose two linear time-varying control laws to achieve trajectory tracking on S-n and show the asymptotic stability of the tracking error. A distributed control is designed for the consensus of multiagent bilinear systems on S-n with an undirected tree as the communication graph. The consensus manifold is shown to have an almost global domain of attraction.