Cell-to-cell variation is a universal feature of life that affects a wide range of biological phenomena, from developmental plasticity to tumour heterogeneity. Although recent advances have improved our ability to document cellular phenotypic variation, the fundamental mechanisms that generate variability from identical DNA sequences remain elusive. Here we reveal the landscape and principles of mammalian DNA regulatory variation by developing a robust method for mapping the accessible genome of individual cells by assay for transposase-accessible chromatin using sequencing (ATAC-seq) integrated into a programmable microfluidics platform. Single-cell ATAC-seq (scATAC-seq) maps from hundreds of single cells in aggregate closely resemble accessibility profiles from tens of millions of cells and provide insights into cell-to-cell variation. Accessibility variance is systematically associated with specific trans-factors and cis-elements, and we discover combinations of trans-factors associated with either induction or suppression of cell-to-cell variability. We further identify sets of trans-factors associated with cell-type-specific accessibility variance across eight cell types. Targeted perturbations of cell cycle or transcription factor signalling evoke stimulus-specific changes in this observed variability. The pattern of accessibility variation in cis across the genome recapitulates chromosome compartments de novo, linking single-cell accessibility variation to three-dimensional genome organization. Single-cell analysis of DNA accessibility provides new insight into cellular variation of the 'regulome'.