The novel coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. The main receptor of SARS-CoV-2, angiotensin I converting enzyme 2 (ACE2), is now undergoing extensive scrutiny to understand the routes of transmission and sensitivity in different species. Here, we utilized a unique dataset of ACE2 sequences from 410 vertebrate species, including 252 mammals, to study the conservation of ACE2 and its potential to be used as a receptor by SARS-CoV-2. We designed a five-category binding score based on the conservation properties of 25 amino acids important for the binding between ACE2 and the SARS-CoV-2 spike protein. Only mammals fell into the medium to very high categories and only catarrhine primates into the very high category, suggesting that they are at high risk for SARS-CoV-2 infection. We employed a protein structural analysis to qualitatively assess whether amino acid changes at variable residues would be likely to disrupt ACE2/SARS-CoV-2 spike protein binding and found the number of predicted unfavorable changes significantly correlated with the binding score. Extending this analysis to human population data, we found only rare (frequency <0.001) variants in 10/25 binding sites. In addition, we found significant signals of selection and accelerated evolution in the ACE2 coding sequence across all mammals, and specific to the bat lineage. Our results, if confirmed by additional experimental data, may lead to the identification of intermediate host species for SARS-CoV-2, guide the selection of animal models of COVID-19, and assist the conservation of animals both in native habitats and in human care.