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We investigate the problem of collaborative video streaming with Raptor network coding over overlay networks. We exploit path and source diversity, as well as basic processing capabilities of network nodes to increase the overall throughput and improve the video quality at the clients. We consider an architecture where several streaming servers simultaneously deliver video information to a set of clients. The servers apply Raptor coding on the video packets for error resiliency, and the forwarding peer nodes further combine the Raptor coded video packets in order to increase the packet diversity in the network. We find the optimal source and channel rate allocation in such a collaborative streaming system. The resulting scheme efficiently exploits the available network resources for improved video quality. The experimental evaluation demonstrates that it typically outperforms Raptor video streaming systems that do not use network coding.