Using single-cell RNA-seq (scRNA-seq), the full transcriptome of individual cells can be acquired, enabling a quantitative cell-type characterisation based on expression profiles. However, due to the large variability in gene expression, identifying cell types based on the transcriptome remains challenging. We present Single-Cell Consensus Clustering (SC3), a tool for unsupervised clustering of scRNA-seq data. SC3 achieves high accuracy and robustness by consistently integrating different clustering solutions through a consensus approach. Tests on twelve published datasets show that SC3 outperforms five existing methods while remaining scalable, as shown by the analysis of a large dataset containing 44,808 cells. Moreover, an interactive graphical implementation makes SC3 accessible to a wide audience of users, and SC3 aids biological interpretation by identifying marker genes, differentially expressed genes and outlier cells. We illustrate the capabilities of SC3 by characterising newly obtained transcriptomes from subclones of neoplastic cells collected from patients.