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 model approach for anytime pixel-level recognition. A cascade of "exits" is attached to the model to make multiple predictions and direct further computation. 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 model with redesigned exit architecture and spatial adaptivity enables anytime inference, achieves the same level of final accuracy, and even significantly reduces total computation. We evaluate our approach on semantic segmentation and human pose estimation. On Cityscapes semantic segmentation and MPII human pose estimation, our approach enables anytime inference while also reducing the total FLOPs of its base models by 44.4% and 59.1% without sacrificing accuracy. As a new anytime baseline, we measure the anytime capability of deep equilibrium networks, a recent class of model that is intrinsically iterative, and we show that the accuracy-computation curve of our architecture strictly dominates it.