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Benefiting from the event-driven and sparse spiking characteristics of the brain, spiking neural networks (SNNs) are becoming an energy-efficient alternative to artificial neural networks (ANNs). However, the performance gap between SNNs and ANNs has been a great hindrance to deploying SNNs ubiquitously for a long time. To leverage the full potential of SNNs, we study the effect of attention mechanisms in SNNs. We first present our idea of attention with a plug-and-play kit, termed the Multi-dimensional Attention (MA). Then, a new attention SNN architecture with end-to-end training called "MA-SNN" is proposed, which infers attention weights along the temporal, channel, as well as spatial dimensions separately or simultaneously. Based on the existing neuroscience theories, we exploit the attention weights to optimize membrane potentials, which in turn regulate the spiking response in a data-dependent way. At the cost of negligible additional parameters, MA facilitates vanilla SNNs to achieve sparser spiking activity, better performance, and energy efficiency concurrently. Experiments are conducted in event-based DVS128 Gesture/Gait action recognition and ImageNet-1k image classification. On Gesture/Gait, the spike counts are reduced by 84.9%/81.6%, and the task accuracy and energy efficiency are improved by 5.9%/4.7% and 3.4$\times$/3.2$\times$. On ImageNet-1K, we achieve top-1 accuracy of 75.92% and 77.08% on single/4-step Res-SNN-104, which are state-of-the-art results in SNNs. To our best knowledge, this is for the first time, that the SNN community achieves comparable or even better performance compared with its ANN counterpart in the large-scale dataset. Our work lights up SNN's potential as a general backbone to support various applications for SNNs, with a great balance between effectiveness and efficiency.