Human-associated microbial communities have a crucial role in determining our health and well-being, and this has led to the continuing development of microbiome-based therapies such as faecal microbiota transplantation. These microbial communities are very complex, dynamic and highly personalized ecosystems, exhibiting a high degree of inter-individual variability in both species assemblages and abundance profiles. It is not known whether the underlying ecological dynamics of these communities, which can be parameterized by growth rates, and intra- and inter-species interactions in population dynamics models, are largely host-independent (that is, universal) or host-specific. If the inter-individual variability reflects host-specific dynamics due to differences in host lifestyle, physiology or genetics, then generic microbiome manipulations may have unintended consequences, rendering them ineffective or even detrimental. Alternatively, microbial ecosystems of different subjects may exhibit universal dynamics, with the inter-individual variability mainly originating from differences in the sets of colonizing species. Here we develop a new computational method to characterize human microbial dynamics. By applying this method to cross-sectional data from two large-scale metagenomic studies--the Human Microbiome Project and the Student Microbiome Project--we show that gut and mouth microbiomes display pronounced universal dynamics, whereas communities associated with certain skin sites are probably shaped by differences in the host environment. Notably, the universality of gut microbial dynamics is not observed in subjects with recurrent Clostridium difficile infection but is observed in the same set of subjects after faecal microbiota transplantation. These results fundamentally improve our understanding of the processes that shape human microbial ecosystems, and pave the way to designing general microbiome-based therapies.