Capturing voxel-wise spatial correspondence across distinct modalities is crucial for medical image analysis. However, current registration approaches are not practical enough in terms of registration accuracy and clinical applicability. In this paper, we introduce MambaMorph, a novel multi-modality deformable registration framework. Specifically, MambaMorph utilizes a Mamba-based registration module and a fine-grained, yet simple, feature extractor for efficient long-range correspondence modeling and high-dimensional feature learning, respectively. Additionally, we develop a well-annotated brain MR-CT registration dataset, SR-Reg, to address the scarcity of data in multi-modality registration. To validate MambaMorph's multi-modality registration capabilities, we conduct quantitative experiments on both our SR-Reg dataset and a public T1-T2 dataset. The experimental results on both datasets demonstrate that MambaMorph significantly outperforms the current state-of-the-art learning-based registration methods in terms of registration accuracy. Further study underscores the efficiency of the Mamba-based registration module and the lightweight feature extractor, which achieve notable registration quality while maintaining reasonable computational costs and speeds. We believe that MambaMorph holds significant potential for practical applications in medical image registration. The code for MambaMorph is available at: https://github.com/Guo-Stone/MambaMorph.