Deep learning-based speech enhancement methods have significantly improved speech quality and intelligibility. Convolutional neural networks (CNNs) have been proven to be essential components of many high-performance models. In this paper, we introduce adaptive convolution, an efficient and versatile convolutional module that enhances the model's capability to adaptively represent speech signals. Adaptive convolution performs frame-wise causal dynamic convolution, generating time-varying kernels for each frame by assembling multiple parallel candidate kernels. A Lightweight attention mechanism leverages both current and historical information to assign adaptive weights to each candidate kernel, guiding their aggregation. This enables the convolution operation to adapt to frame-level speech spectral features, leading to more efficient extraction and reconstruction. Experimental results on various CNN-based models demonstrate that adaptive convolution significantly improves the performance with negligible increases in computational complexity, especially for lightweight models. Furthermore, we propose the adaptive convolutional recurrent network (AdaptCRN), an ultra-lightweight model that incorporates adaptive convolution and an efficient encoder-decoder design, achieving superior performance compared to models with similar or even higher computational costs.