Genomes are transmitted faithfully from dividing cells to their offspring. Changes that occur during DNA repair, chromosome duplication, and transmission or via recombination provide a natural source of genetic variation. They occur at low frequency because of the intrinsic variable nature of genomes, which we refer to as genome instability. However, genome instability can be enhanced by exposure to external genotoxic agents or as the result of cellular pathologies. We review the causes of genome instability as well as how it results in hyper-recombination, genome rearrangements, and chromosome fragmentation and loss, which are mainly mediated by double-strand breaks or single-strand gaps. Such events are primarily associated with defects in DNA replication and the DNA damage response, and show high incidence at repetitive DNA, non-B DNA structures, DNA-protein barriers, and highly transcribed regions. Identifying the causes of genome instability is crucial to understanding genome dynamics during cell proliferation and its role in cancer, aging, and a number of rare genetic diseases.