Shifts in rainfall patterns and increasing temperatures associated with climate change are likely to cause widespread forest decline in regions where droughts are predicted to increase in duration and severity. One primary cause of productivity loss and plant mortality during drought is hydraulic failure. Drought stress creates trapped gas emboli in the water transport system, which reduces the ability of plants to supply water to leaves for photosynthetic gas exchange and can ultimately result in desiccation and mortality. At present we lack a clear picture of how thresholds to hydraulic failure vary across a broad range of species and environments, despite many individual experiments. Here we draw together published and unpublished data on the vulnerability of the transport system to drought-induced embolism for a large number of woody species, with a view to examining the likely consequences of climate change for forest biomes. We show that 70% of 226 forest species from 81 sites worldwide operate with narrow (<1 megapascal) hydraulic safety margins against injurious levels of drought stress and therefore potentially face long-term reductions in productivity and survival if temperature and aridity increase as predicted for many regions across the globe. Safety margins are largely independent of mean annual precipitation, showing that there is global convergence in the vulnerability of forests to drought, with all forest biomes equally vulnerable to hydraulic failure regardless of their current rainfall environment. These findings provide insight into why drought-induced forest decline is occurring not only in arid regions but also in wet forests not normally considered at drought risk.