A major focus of clinical imaging workflow is disease diagnosis and management, leading to medical imaging datasets strongly tied to specific clinical objectives. This scenario has led to the prevailing practice of developing task-specific segmentation models, without gaining insights from widespread imaging cohorts. Inspired by the training program of medical radiology residents, we propose a shift towards universal medical image segmentation, a paradigm aiming to leverage the diversity and commonality across clinical targets, body regions, and imaging modalities. Towards this goal, we develop Hermes, a novel context-prior learning approach to address the challenges of data heterogeneity and annotation differences in medical image segmentation. In a large collection of eleven diverse datasets (2,438 3D images) across five modalities (CT, PET, T1, T2 and cine MRI) and multiple body regions, we demonstrate the merit of the universal paradigm over the traditional paradigm on addressing multiple tasks within a single model. By exploiting the synergy across a spectrum of tasks, Hermes achieves state-of-the-art performance on all testing datasets and shows superior model scalability. Investigation on two additional datasets reveals Hermes' strong performance for transfer learning, incremental learning, and generalization to downstream tasks. Hermes's learned priors demonstrate an appealing trait to reflect the intricate relations among tasks and modalities, which well aligns with the established anatomical and imaging principles in radiology. The code and model will be made publicly available.