Internet-based cloud computing is a new computing paradigm aiming to provide agile and scalable resource access in a utility-like fashion. Other than being an ideal platform for computation-intensive tasks, clouds are believed to be also suitable to support large-scale applications with periods of flash crowds by providing elastic amounts of bandwidth and other resources on the fly. The fundamental question is how to configure the cloud utility to meet the highly dynamic demands of such applications at a modest cost. In this paper, we address this practical issue with solid theoretical analysis and efficient algorithm design using Video on Demand (VoD) as the example application. Having intensive bandwidth and storage demands in real time, VoD applications are purportedly ideal candidates to be supported on a cloud platform, where the on-demand resource supply of the cloud meets the dynamic demands of the VoD applications. We introduce a queueing network based model to characterize the viewing behaviors of users in a multichannel VoD application, and derive the server capacities needed to support smooth playback in the channels for two popular streaming models: client-server and P2P. We then propose a dynamic cloud resource provisioning algorithm which, using the derived capacities and instantaneous network statistics as inputs, can effectively support VoD streaming with low cloud utilization cost. Our analysis and algorithm design are verified and extensively evaluated using large-scale experiments under dynamic realistic settings on a home-built cloud platform.