Predicted changes in the global climate are likely to cause large shifts in the geographic ranges of many plant and animal species. To date, predictions of future range shifts have relied on a variety of modeling approaches with different levels of model accuracy. Using a common data set, we investigated the potential implications of alternative modeling approaches for conclusions about future range shifts and extinctions. Our common data set entailed the current ranges of 100 randomly selected mammal species found in the western hemisphere. Using these range maps, we compared six methods for modeling predicted future ranges. Predicted future distributions differed markedly across the alternative modeling approaches, which in turn resulted in estimates of extinction rates that ranged between 0% and 7%, depending on which model was used. Random forest predictors, a model-averaging approach, consistently outperformed the other techniques (correctly predicting >99% of current absences and 86% of current presences). We conclude that the types of models used in a study can have dramatic effects on predicted range shifts and extinction rates; and that model-averaging approaches appear to have the greatest potential for predicting range shifts in the face of climate change.