The human gut harbors a large and complex community of beneficial microbes that remain stable over long periods. This stability is considered critical for good health but is poorly understood. Here we develop a body of ecological theory to help us understand microbiome stability. Although cooperating networks of microbes can be efficient, we find that they are often unstable. Counterintuitively, this finding indicates that hosts can benefit from microbial competition when this competition dampens cooperative networks and increases stability. More generally, stability is promoted by limiting positive feedbacks and weakening ecological interactions. We have analyzed host mechanisms for maintaining stability—including immune suppression, spatial structuring, and feeding of community members—and support our key predictions with recent data.