Nonhomologous end joining (NHEJ), the direct rejoining of DNA double-strand breaks, is closely associated with illegitimate recombination and chromosomal rearrangement. This has led to the concept that NHEJ is error prone. Studies with the yeast Saccharomyces cerevisiae have revealed that this model eukaryote has a classical NHEJ pathway dependent on Ku and DNA ligase IV, as well as alternative mechanisms for break rejoining. The evolutionary conservation of the Ku-dependent process includes several genes dedicated to this pathway, indicating that classical NHEJ at least is a strong contributor to fitness in the wild. Here we review how double-strand break structure, the yeast NHEJ proteins, and alternative rejoining mechanisms influence the accuracy of break repair. We also consider how the balance between NHEJ and homologous repair is regulated by cell state to promote genome preservation. The principles discussed are instructive to NHEJ in all organisms.