Existing salient object detection (SOD) models primarily resort to convolutional neural networks (CNNs) and Transformers. However, the limited receptive fields of CNNs and quadratic computational complexity of transformers both constrain the performance of current models on discovering attention-grabbing objects. The emerging state space model, namely Mamba, has demonstrated its potential to balance global receptive fields and computational complexity. Therefore, we propose a novel unified framework based on the pure Mamba architecture, dubbed saliency Mamba (Samba), to flexibly handle general SOD tasks, including RGB/RGB-D/RGB-T SOD, video SOD (VSOD), and RGB-D VSOD. Specifically, we rethink Mamba's scanning strategy from the perspective of SOD, and identify the importance of maintaining spatial continuity of salient patches within scanning sequences. Based on this, we propose a saliency-guided Mamba block (SGMB), incorporating a spatial neighboring scanning (SNS) algorithm to preserve spatial continuity of salient patches. Additionally, we propose a context-aware upsampling (CAU) method to promote hierarchical feature alignment and aggregations by modeling contextual dependencies. Experimental results show that our Samba outperforms existing methods across five SOD tasks on 21 datasets with lower computational cost, confirming the superiority of introducing Mamba to the SOD areas. Our code will be made publicly available.