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We compute a series of three-dimensional general relativistic magnetohydrodynamic simulations of accretion flows in the Kerr metric to investigate the properties of the unbound outflows that result. The overall strength of these outflows increases sharply with increasing black hole rotation rate, but a number of generic features are found in all cases. The mass in the outflow is concentrated in a hollow cone whose opening angle is largely determined by the effective potential for matter orbiting with angular momentum comparable to that of the innermost stable circular orbit. The dominant force accelerating the matter outward comes from the pressure of the accretion disk's corona. The principal element that shapes the outflow is therefore the centrifugal barrier preventing accreting matter from coming close to the rotation axis. Inside the centrifugal barrier, the cone contains very little matter and is dominated by electromagnetic fields that rotate at a rate tied closely to the rotation of the black hole. These fields carry an outward-going Poynting flux whose immediate energy source is the rotating spacetime of the Kerr black hole. When the spin parameter a/M of the black hole exceeds ~0.9, the energy carried to infinity by these outflows can be comparable to the nominal radiative efficiency predicted in the Novikov-Thorne model. Similarly, the expelled angular momentum can be comparable to that accreted by the black hole. Both the inner electromagnetic part and the outer matter part can contribute in significant fashion to the energy and angular momentum of the outflow.