Single-cell RNA-sequencing (scRNA-seq) is a powerful approach for reconstructing cellular differentiation trajectories. However, inferring both the state and direction of differentiation without prior knowledge has remained challenging. Here we describe a simple yet robust determinant of developmental potential—the number of detectably expressed genes per cell—and leverage this measure of transcriptional diversity to develop a new framework for predicting ordered differentiation states from scRNA-seq data. When evaluated on ~150,000 single-cell transcriptomes spanning 53 lineages and five species, our approach, called CytoTRACE, outperformed previous methods and ~19,000 molecular signatures for resolving experimentally-confirmed developmental trajectories. In addition, it enabled unbiased identification of tissue-resident stem cells, including cells with long-term regenerative potential. When used to analyze human breast tumors, we discovered candidate genes associated with less-differentiated luminal progenitor cells and validated GULP1 as a novel gene involved in tumorigenesis. Our study establishes a key RNA-based correlate of developmental potential and provides a new platform for robust delineation of cellular hierarchies (https://cytotrace.stanford.edu).