Super-resolution ultrasound microvessel imaging based on ultrasound localization microscopy (ULM) is an emerging imaging modality that is capable of resolving micrometer-scaled vessels deep into tissue. In practice, ULM is limited by the need for contrast injection, long data acquisition, and computationally expensive postprocessing times. In this study, we present a contrast-free super-resolution power Doppler (CS-PD) technique that uses deep networks to achieve super-resolution with short data acquisition. The training dataset is comprised of spatiotemporal ultrafast ultrasound signals acquired from in vivo mouse brains, while the testing dataset includes in vivo mouse brain, chicken embryo chorioallantoic membrane (CAM), and healthy human subjects. The in vivo mouse imaging studies demonstrate that CS-PD could achieve an approximate twofold improvement in spatial resolution when compared with conventional power Doppler. In addition, the microvascular images generated by CS-PD showed good agreement with the corresponding ULM images as indicated by a structural similarity index of 0.7837 and a peak signal-to-noise ratio (PSNR) of 25.52. Moreover, CS-PD was able to preserve the temporal profile of the blood flow (e.g., pulsatility) that is similar to conventional power Doppler. Finally, the generalizability of CS-PD was demonstrated on testing data of different tissues using different imaging settings. The fast inference time of the proposed deep neural network also allows CS-PD to be implemented for real-time imaging. These features of CS-PD offer a practical, fast, and robust microvascular imaging solution for many preclinical and clinical applications of Doppler ultrasound.