The proliferation of multi-source remote sensing data has propelled the development of deep learning for dense prediction, yet significant challenges in data and task unification persist. Current deep learning architectures for remote sensing are fundamentally rigid. They are engineered for fixed input-output configurations, restricting their adaptability to the heterogeneous spatial, temporal, and spectral dimensions inherent in real-world data. Furthermore, these models neglect the intrinsic correlations among semantic segmentation, binary change detection, and semantic change detection, necessitating the development of distinct models or task-specific decoders. This paradigm is also constrained to a predefined set of output semantic classes, where any change to the classes requires costly retraining. To overcome these limitations, we introduce the Spatial-Temporal-Spectral Unified Network (STSUN) for unified modeling. STSUN can adapt to input and output data with arbitrary spatial sizes, temporal lengths, and spectral bands by leveraging their metadata for a unified representation. Moreover, STSUN unifies disparate dense prediction tasks within a single architecture by conditioning the model on trainable task embeddings. Similarly, STSUN facilitates flexible prediction across multiple set of semantic categories by integrating trainable category embeddings as metadata. Extensive experiments on multiple datasets with diverse Spatial-Temporal-Spectral configurations in multiple scenarios demonstrate that a single STSUN model effectively adapts to heterogeneous inputs and outputs, unifying various dense prediction tasks and diverse semantic class predictions. The proposed approach consistently achieves state-of-the-art performance, highlighting its robustness and generalizability for complex remote sensing applications.