Many neural networks exhibit stability in their activation patterns over time in response to inputs from sensors operating under real-world conditions. By capitalizing on this property of natural signals, we propose a Recurrent Neural Network (RNN) architecture called a delta network in which each neuron transmits its value only when the change in its activation exceeds a threshold. The execution of RNNs as delta networks is attractive because their states must be stored and fetched at every timestep, unlike in convolutional neural networks (CNNs). We show that a naive run-time delta network implementation offers modest improvements on the number of memory accesses and computes, but optimized training techniques confer higher accuracy at higher speedup. With these optimizations, we demonstrate a 9X reduction in cost with negligible loss of accuracy for the TIDIGITS audio digit recognition benchmark. Similarly, on the large Wall Street Journal (WSJ) speech recognition benchmark, pretrained networks can also be greatly accelerated as delta networks and trained delta networks show a 5.7x improvement with negligible loss of accuracy. Finally, on an end-to-end CNN-RNN network trained for steering angle prediction in a driving dataset, the RNN cost can be reduced by a substantial 100X.