Human pluripotent stem cells (hPS cells) can self-renew indefinitely, making them an attractive source for regenerative therapies. This expansion potential has been linked with the acquisition of large copy number variants that provide mutated cells with a growth advantage in culture. The nature, extent and functional effects of other acquired genome sequence mutations in cultured hPS cells are not known. Here we sequence the protein-coding genes (exomes) of 140 independent human embryonic stem cell (hES cell) lines, including 26 lines prepared for potential clinical use. We then apply computational strategies for identifying mutations present in a subset of cells in each hES cell line. Although such mosaic mutations were generally rare, we identified five unrelated hES cell lines that carried six mutations in the TP53 gene that encodes the tumour suppressor P53. The TP53 mutations we observed are dominant negative and are the mutations most commonly seen in human cancers. We found that the TP53 mutant allelic fraction increased with passage number under standard culture conditions, suggesting that the P53 mutations confer selective advantage. We then mined published RNA sequencing data from 117 hPS cell lines, and observed another nine TP53 mutations, all resulting in coding changes in the DNA-binding domain of P53. In three lines, the allelic fraction exceeded 50%, suggesting additional selective advantage resulting from the loss of heterozygosity at the TP53 locus. As the acquisition and expansion of cancer-associated mutations in hPS cells may go unnoticed during most applications, we suggest that careful genetic characterization of hPS cells and their differentiated derivatives be carried out before clinical use.