Continual Learning (CL) aims to incrementally update a trained model on new tasks without forgetting the acquired knowledge of old ones. Existing CL methods usually reduce forgetting with task priors, \ie using task identity or a subset of previously seen samples for model training. However, these methods would be infeasible when such priors are unknown in real-world applications. To address this fundamental but seldom-studied problem, we propose a Prior-Free Continual Learning (PFCL) method, which learns new tasks without knowing the task identity or any previous data. First, based on a fixed single-head architecture, we eliminate the need for task identity to select the task-specific output head. Second, we employ a regularization-based strategy for consistent predictions between the new and old models, avoiding revisiting previous samples. However, using this strategy alone often performs poorly in class-incremental scenarios, particularly for a long sequence of tasks. By analyzing the effectiveness and limitations of conventional regularization-based methods, we propose enhancing model consistency with an auxiliary unlabeled dataset additionally. Moreover, since some auxiliary data may degrade the performance, we further develop a reliable sample selection strategy to obtain consistent performance improvement. Extensive experiments on multiple image classification benchmark datasets show that our PFCL method significantly mitigates forgetting in all three learning scenarios. Furthermore, when compared to the most recent rehearsal-based methods that replay a limited number of previous samples, PFCL achieves competitive accuracy. Our code is available at: https://github.com/visiontao/pfcl