Most human cancer cells show signs of genome instability, ranging from elevated mutation rates to gross chromosomal rearrangements and alterations in chromosome number. Little is known about the molecular mechanisms that generate this instability or how it is suppressed in normal cells. Recent studies of the yeast Saccharomyces cerevisiae have begun to uncover the extensive and redundant pathways that keep the rate of genome rearrangements at very low levels. These studies, which we review here, have implicated more than 50 genes in the suppression of genome instability, including genes that function in S-phase checkpoints, recombination pathways, and telomere maintenance. Human homologs of several of these genes have well-established roles as tumor suppressors, consistent with the hypothesis that the mechanisms preserving genome stability in yeast are the same mechanisms that go awry in cancer.