We investigate relationships between life history traits and the character of population dynamics as revealed by time series data. Our classification of time series is according to ‘extinction category,’ where we identify three classes of populations: (i) weakly varying populations with such high growth rates that long-term persistence is likely (unless some extreme catastrophe occurs); (ii) populations with such low growth rates that average population size must be large to buffer them against extinction in a variable environment; and (iii) highly variable populations that fluctuate so dramatically that dispersal or some other refuge mechanism is likely to be key to their avoidance of extinction. Using 1941 time series representing 758 species from the Global Population Dynamics Database, we find that, depending on the form of density dependence one assumes, between 46 and 90% of species exhibit dynamics that are so variable that even large carrying capacities could not buffer them against extinction on a 100-year time horizon. The fact that such a large proportion of population dynamics are so locally variable vindicates the growing realization that dispersal, habitat connectedness, and large-scale processes are key to local persistence. Furthermore, for mammals, simply by knowing body size, age at first reproduction, and average number of offspring we could correctly predict extinction categories for 83% of species (60 of 72).