DNA replication initiates from replication origins firing throughout S phase. Debate remains about whether origins are a fixed set of loci, or a loose agglomeration of potential sites used stochastically in individual cells, and about how consistent their firing time is. We develop an approach to profile DNA replication from whole-genome sequencing of thousands of single cells, which includes in silico flow cytometry, a method for discriminating replicating and non-replicating cells. Using two microfluidic platforms, we analyze up to 2437 replicating cells from a single sample. The resolution and scale of the data allow focused analysis of replication initiation sites, demonstrating that most occur in confined genomic regions. While initiation order is remarkably similar across cells, we unexpectedly identify several subtypes of initiation regions in late-replicating regions. Taken together, high throughput, high resolution sequencing of individual cells reveals previously underappreciated variability in replication initiation and progression.