In the burgeoning field of single-cell transcriptomics, a pressing challenge is to benchmark various experimental protocols and numerous computational methods in an unbiased manner. Although dozens of simulators have been developed for single-cell RNA-seq (scRNA-seq) data, they lack the capacity to simultaneously achieve all the three goals: preserving genes, capturing gene correlations, and generating any number of cells with varying sequencing depths. To fill in this gap, here we propose scDesign2, an interpretable simulator that achieves all the three goals and generates high-fidelity synthetic data for multiple scRNA-seq protocols and other single-cell gene expression count-based technologies. Compared with existing simulators, scDesign2 is advantageous in its transparent use of probabilistic models and is unique in its ability to capture gene correlations via copula. We verify that scDesign2 generates more realistic synthetic data for four scRNA-seq protocols (10x Genomics, CEL-Seq2, Fluidigm C1, and Smart-Seq2) and two single-cell spatial transcriptomics protocols (MERFISH and pciSeq) than existing simulators do. Under two typical computational tasks, cell clustering and rare cell type detection, we demonstrate that scDesign2 provides informative guidance on deciding the optimal sequencing depth and cell number in single-cell RNA-seq experimental design, and that scDesign2 can effectively benchmark computational methods under varying sequencing depths and cell numbers. With these advantages, scDesign2 is a powerful tool for single-cell researchers to design experiments, develop computational methods, and choose appropriate methods for specific data analysis needs.