Anytime inference requires a model to make a progression of predictions which might be halted at any time. Prior research on anytime visual recognition has mostly focused on image classification.We propose the first unified and end-to-end approach for anytime dense prediction. A cascade of "exits" is attached to the model to make multiple predictions. We redesign the exits to account for the depth and spatial resolution of the features for each exit. To reduce total computation, and make full use of prior predictions, we develop a novel spatially adaptive approach to avoid further computation on regions where early predictions are already sufficiently confident. Our full method, named anytime dense prediction with confidence (ADP-C), achieves the same level of final accuracy, and meanwhile significantly reduces total computation. We evaluate our method on Cityscapes semantic segmentation and MPII human pose estimation: ADP-C enables anytime inference without sacrificing accuracy while also reducing the total FLOPs of its base models by 44.4% and 59.1%. We compare with anytime inference by deep equilibrium networks and feature-based stochastic sampling, showing that ADP-C dominates both across the accuracy-computation curve. Our code is available at https://github.com/liuzhuang13/anytime.