The gut microbiome is a modifier of disease risk because it interacts with nutrition, metabolism, immunity and infection. Aging-related health loss has been correlated with transition to different microbiome states. Microbiome summary indices including alpha diversity are apparently useful to describe these states but belie taxonomic differences that determine biological importance. We analyzed 21,000 fecal microbiomes from seven data repositories, across five continents spanning participant ages 18-107 years, revealing that microbiome diversity and uniqueness correlate with aging, but not healthy aging. Among summary statistics tested, only Kendall uniqueness accurately reflects loss of the core microbiome and the abundance and ranking of disease-associated and health-associated taxa. Increased abundance of these disease-associated taxa and depletion of a coabundant subset of health-associated taxa are a generic feature of aging. These alterations are stronger correlates of unhealthy aging than most microbiome summary statistics and thus help identify better targets for therapeutic modulation of the microbiome.