We model the effects of demographic and environmental stochasticity in the logistic, Gompertz and Ricker models. We focus on factors affecting extinction risk in a single population as well as in pairs of competing populations. A thorough numerical analysis of extinction probability is given. We find that colored environmental noise causes reductions in extinction risk, and that correlation between the environmental noise experienced by two competing populations increases extinction risk. The Ricker model exhibits a high rate of persistence in comparison with the logistic and Gompertz models.