A key concern for conservation biologists is whether populations of plants and animals are likely to fluctuate widely in number or remain relatively stable around some steady-state value. In our study of 634 populations of mammals, birds, fish and insects, we find that most can be expected to remain stable despite year to year fluctuations caused by environmental factors. Mean return rates were generally around one but were higher in insects (1.09 ± 0.02 SE) and declined with body size in mammals. In general, this is good news for conservation, as stable populations are less likely to go extinct. However, the lower return rates of the large mammals may make them more vulnerable to extinction. Our estimates of return rates were generally well below the threshold for chaos, which makes it unlikely that chaotic dynamics occur in natural populations – one of ecology’s key unanswered questions.