A key challenge in studying organisms and diseases is to detect rare molecular programs and rare cell populations (RCPs) that drive development, differentiation, and transformation. Molecular features such as genes and proteins defining RCPs are often unknown and difficult to detect from unenriched single-cell data, using conventional dimensionality reduction and clustering-based approaches. Here, we propose an unsupervised approach, SCMER (Single-Cell Manifold presERving feature selection), which selects a compact set of molecular features with definitive meanings that preserve the manifold of the data. We applied SCMER in the context of hematopoiesis, lymphogenesis, tumorigenesis, and drug resistance and response. We found that SCMER can identify non-redundant features that sensitively delineate both common cell lineages and rare cellular states. SCMER can be used for discovering molecular features in a high dimensional dataset, designing targeted, cost-effective assays for clinical applications, and facilitating multi-modality integration.