Understanding the influence of environmental variability on population dynamics is a fundamental goal of ecology. Theory suggests that, for populations in variable environments, temporal correlations between demographic vital rates (e.g., growth, survival, reproduction) can increase (if positive) or decrease (if negative) the variability of year-to-year population growth. Because this variability generally decreases long-term population viability, vital rate correlations may importantly affect population dynamics in stochastic environments. Despite long-standing theoretical interest, it is unclear whether vital rate correlations are common in nature, whether their directions are predominantly negative or positive, and whether they are of sufficient magnitude to warrant broad consideration in studies of stochastic population dynamics. We used long-term demographic data for three perennial plant species, hierarchical Bayesian parameterization of population projection models, and stochastic simulations to address the following questions: (1) What are the sign, magnitude, and uncertainty of temporal correlations between vital rates? (2) How do specific pairwise correlations affect the year-to-year variability of population growth? (3) Does the net effect of all vital rate correlations increase or decrease year-to-year variability? (4) What is the net effect of vital rate correlations on the long-term stochastic population growth rate (λS)? We found only four moderate to strong correlations, both positive and negative in sign, across all species and vital rate pairs; otherwise, correlations were generally weak in magnitude and variable in sign. The net effect of vital rate correlations ranged from a slight decrease to an increase in the year-to-year variability of population growth, with average changes in variance ranging from -1% to +22%. However, vital rate correlations caused virtually no change in the estimates of λS (mean effects ranging from -0.01% to +0.17%). Therefore, the proportional changes in the variance of population growth caused by demographic correlations were too small on an absolute scale to importantly affect population growth and viability. We conclude that in our three focal populations and perhaps more generally, vital rate correlations have little effect on stochastic population dynamics. This may be good news for population ecologists, because estimating vital rate correlations and incorporating them into population models can be data-intensive and technically challenging.