We examine the scaling law B=cM^α which connects organismal resting metabolic rate B with organismal mass M, where α is commonly held to be 3/4. Since simple dimensional analysis suggests α=2/3, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting α=2/3 in favor of α=3/4. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in α. We also review theoretical justifications of α=3/4 based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for α=3/4 require assumptions that render them unconvincing for rejecting the null hypothesis that α=2/3.