We present co-skeletons, a new method that computes consistent curve skeletons for 3D shapes from a given family. We compute co-skeletons in terms of sampling density and semantic relevance, while preserving the desired characteristics of traditional, per-shape curve skeletonization approaches. We take the curve skeletons extracted by traditional approaches for all shapes from a family as input, and compute semantic correlation information of individual skeleton branches to guide an edge-pruning process via skeleton-based descriptors, clustering, and a voting algorithm. Our approach achieves more concise and family-consistent skeletons when compared to traditional per-shape methods. We show the utility of our method by using co-skeletons for shape segmentation and shape blending on real-world data.