In this paper we show how PRAM algorithms can be turned into efficient streaming algorithms for several classical combinatorial problems in theW-Stream model. In this model, at each pass one input stream is read and one output stream is written; streams are pipelined in such a way that the output stream produced at pass i is given as input stream at pass i + 1. Our techniques yield near-optimal algorithms (up to polylog factors) for several classical problems in this model including sorting, connectivity, minimum spanning tree, biconnected components, and maximal independent set.