Dendritic computation endows biological neurons with rich nonlinear integration and high representational capacity, yet it is largely missing in existing deep spiking neural networks (SNNs). Although detailed multi-compartment models can capture dendritic computations, their high computational cost and limited flexibility make them impractical for deep learning. To combine the advantages of dendritic computation and deep network architectures for a powerful, flexible and efficient computational model, we propose the dendritic spiking neuron (DendSN). DendSN explicitly models dendritic morphology and nonlinear integration in a streamlined design, leading to substantially higher expressivity than point neurons and wide compatibility with modern deep SNN architectures. Leveraging the efficient formulation and high-performance Triton kernels, dendritic SNNs (DendSNNs) can be efficiently trained and easily scaled to deeper networks. Experiments show that DendSNNs consistently outperform conventional SNNs on classification tasks. Furthermore, inspired by dendritic modulation and synaptic clustering, we introduce the dendritic branch gating (DBG) algorithm for task-incremental learning, which effectively reduces inter-task interference. Additional evaluations show that DendSNNs exhibit superior robustness to noise and adversarial attacks, along with improved generalization in few-shot learning scenarios. Our work firstly demonstrates the possibility of training deep SNNs with multiple nonlinear dendritic branches, and comprehensively analyzes the impact of dendrite computation on representation learning across various machine learning settings, thereby offering a fresh perspective on advancing SNN design.