In the past decades, deep neural networks, particularly convolutional neural networks, have achieved state-of-the-art performance in a variety of medical image segmentation tasks. Recently, the introduction of the vision transformer (ViT) has significantly altered the landscape of deep segmentation models. There has been a growing focus on ViTs, driven by their excellent performance and scalability. However, we argue that the current design of the vision transformer-based UNet (ViT-UNet) segmentation models may not effectively handle the heterogeneous appearance (e.g., varying shapes and sizes) of objects of interest in medical image segmentation tasks. To tackle this challenge, we present a structured approach to introduce spatially dynamic components to the ViT-UNet. This adaptation enables the model to effectively capture features of target objects with diverse appearances. This is achieved by three main components: \textbf{(i)} deformable patch embedding; \textbf{(ii)} spatially dynamic multi-head attention; \textbf{(iii)} deformable positional encoding. These components were integrated into a novel architecture, termed AgileFormer. AgileFormer is a spatially agile ViT-UNet designed for medical image segmentation. Experiments in three segmentation tasks using publicly available datasets demonstrated the effectiveness of the proposed method. The code is available at \href{https://github.com/sotiraslab/AgileFormer}{https://github.com/sotiraslab/AgileFormer}.