Large-scale recovery of genomes from isolates, single cells, and metagenomic data has been made possible by advances in computational methods and substantial reductions in sequencing costs. Although this increasing breadth of draft genomes is providing key information regarding the evolutionary and functional diversity of microbial life, it has become impractical to finish all available reference genomes. Making robust biological inferences from draft genomes requires accurate estimates of their completeness and contamination. Current methods for assessing genome quality are ad hoc and generally make use of a limited number of "marker" genes conserved across all bacterial or archaeal genomes. Here we introduce CheckM, an automated method for assessing the quality of a genome using a broader set of marker genes specific to the position of a genome within a reference genome tree and information about the collocation of these genes. We demonstrate the effectiveness of CheckM using synthetic data and a wide range of isolate-, single-cell-, and metagenome-derived genomes. CheckM is shown to provide accurate estimates of genome completeness and contamination and to outperform existing approaches. Using CheckM, we identify a diverse range of errors currently impacting publicly available isolate genomes and demonstrate that genomes obtained from single cells and metagenomic data vary substantially in quality. In order to facilitate the use of draft genomes, we propose an objective measure of genome quality that can be used to select genomes suitable for specific gene- and genome-centric analyses of microbial communities.