Adaptation of arm movements to laterally displacing prism glasses is usually highly specific to body part and movement type and is known to require the cerebellum. Here, we show that prism adaptation of walking trajectory generalizes to reaching (a different behavior involving a different body part) and that this adaptation requires the cerebellum. In experiment 1, healthy control subjects adapted to prisms during either reaching or walking and were tested for generalization to the other movement type. We recorded lateral deviations in finger endpoint position and walking direction to measure negative aftereffects and generalization. Results showed that generalization of prism adaptation is asymmetric: walking generalizes extensively to reaching, but reaching does not generalize to walking. In experiment 2, we compared the performance of cerebellar subjects versus healthy controls during the prism walking adaptation. We measured rates of adaptation, aftereffects, and generalization. Cerebellar subjects had reduced adaptation magnitudes, slowed adaptation rates, decreased negative aftereffects, and poor generalization. Based on these experiments, we propose that prism adaptation during whole body movements through space invokes a more general system for visuomotor remapping, involving recalibration of higher-order, effector-independent brain regions. In contrast, prism adaptation during isolated movements of the limbs is probably recalibrated by effector-specific mechanisms. The cerebellum is an essential component in the network for both types of prism adaptation.