Pluripotent cells of the early embryo, to which embryonic stem cells (ESCs) correspond, give rise to all the somatic cells of the developing fetus. Any defects that occur in their genome or epigenome would have devastating consequences. Genetic and epigenetic change in human ESCs appear to be an inevitable consequence of long-term culture, driven by selection of variant cells that have a higher propensity for self-renewal rather than either differentiation or death. Mechanisms underlying the potentially separate events of mutation and subsequent selection of variants are poorly understood. Here, we show that human ESCs and their malignant counterpart, embryonal carcinoma (EC) cells, both fail to activate critical S-phase checkpoints when exposed to DNA replication inhibitors and commit to apoptosis instead. Human ESCs and EC cells also fail to form replication protein A, cH2AX, or RAD51 foci or load topoisomerase (DNA) II binding protein 1 onto chromatin in response to replication inhibitors. Furthermore, direct measurements of single-stranded DNA (ssDNA) show that these cells fail to generate the ssDNA regions in response to replication stress that are necessary for the activation of checkpoints and the initiation of homologous recombination repair to protect replication fork integrity and restart DNA replication. Taken together, our data suggest that pluripotent cells control genome integrity by the elimination of damaged cells through apoptosis rather than DNA repair, and therefore, mutations or epigenetic modifications resulting in an imbalance in cell death control could lead to genetic instability.