We study the problem of data propagation in sensor networks, comprised of a large number of very small and low-cost nodes, capable of sensing, communicating and computing. The distributed co-operation of such nodes may lead to the accomplishment of large sensing tasks, having useful applications in practice. We present a new protocol for data propagation towards a control center (``sink") that avoids flooding by probabilistically favoring certain (``close to optimal") data transmissions. This protocol is very simple to implement in sensor devices and operates under total absence of co-ordination between sensors. We consider a network model of randomly deployed sensors of sufficient density. As shown by a geometry analysis, the protocol is correct, since it always propagates data to the sink, under ideal network conditions (no failures). Using stochastic processes, we show that the protocol is very energy efficient. Also, when part of the network is inoperative, the protocol manages to propagate data very close to the sink, thus in this sense it is robust. We finally present and discuss large-scale experimental findings validating the analytical results.