The design of algorithms that can run unchanged yet efficiently on a variety of machines characterized by different degrees of parallelism and communication capabilities is a highly desirable goal. We propose a framework for network-obliviousness based on a model of computation where the only parameter is the problem's input size. Algorithms are then evaluated on a model with two parameters, capturing parallelism and granularity of communication. We show that, for a wide class of network-oblivious algorithms, optimality in the latter model implies optimality in a block-variant of the decomposable BSP model, which effectively describes a wide and significant class of parallel platforms. We illustrate our framework by providing optimal network-oblivious algorithms for a few key problems, and also establish some negative results.