Induced pluripotent stem cells (iPSCs) and embryonic stem cells (ESCs) are two types of pluripotent stem cells that hold great promise for biomedical research and medical applications. iPSCs were initially favorably compared to ESCs. This view was first based on ethical arguments (the generation of iPSCs does not require the destruction of an embryo) and on immunological reasons (it is easier to derive patient HLA-matched iPSCs than ESCs). However, several reports suggest that iPSCs might be characterized by higher occurrence of epigenetic and genetic aberrations than ESCs as a consequence of the reprogramming process. We focus here on the DNA integrity of pluripotent stem cells and examine the three main sources of genomic abnormalities in iPSCs: (1) genomic variety of the parental cells, (2) cell reprogramming, and (3) in vitro cell culture. Recent reports claim that it is possible to generate mouse or human iPSC lines with a mutation level similar to that of the parental cells, suggesting that "genome-friendly" reprogramming techniques can be developed. The issue of iPSC DNA integrity clearly highlights the crucial need of guidelines to define the acceptable level of genomic integrity of pluripotent stem cells for biomedical applications. We discuss here the main issues that such guidelines should address.