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Existing RGB-D salient object detection (SOD) models usually treat RGB and depth as independent information and design separate networks for feature extraction from each. Such schemes can easily be constrained by a limited amount of training data or over-reliance on an elaborately designed training process. Inspired by the observation that RGB and depth modalities actually present certain commonality in distinguishing salient objects, a novel joint learning and densely cooperative fusion (JL-DCF) architecture is designed to learn from both RGB and depth inputs through a shared network backbone, known as the Siamese architecture. In this paper, we propose two effective components: joint learning (JL), and densely cooperative fusion (DCF). The JL module provides robust saliency feature learning by exploiting cross-modal commonality via a Siamese network, while the DCF module is introduced for complementary feature discovery. Comprehensive experiments using five popular metrics show that the designed framework yields a robust RGB-D saliency detector with good generalization. As a result, JL-DCF significantly advances the state-of-the-art models by an average of ~2.0% (max F-measure) across seven challenging datasets. In addition, we show that JL-DCF is readily applicable to other related multi-modal detection tasks, including RGB-T (thermal infrared) SOD and video SOD, achieving comparable or even better performance against state-of-the-art methods. We also link JL-DCF to the RGB-D semantic segmentation field, showing its capability of outperforming several semantic segmentation models on the task of RGB-D SOD. These facts further confirm that the proposed framework could offer a potential solution for various applications and provide more insight into the cross-modal complementarity task.