This paper reports an analysis and comparison of the use of 51 different similarity coefficients for computing the similarities between binary fingerprints for both simulated and real chemical data sets. Five pairs and a triplet of coefficients were found to yield identical similarity values, leading to the elimination of seven of the coefficients. The remaining 44 coefficients were then compared in two ways: by their theoretical characteristics using simple descriptive statistics, correlation analysis, multidimensional scaling, Hasse diagrams, and the recently described atemporal target diffusion model; and by their effectiveness for similarity-based virtual screening using MDDR, WOMBAT, and MUV data. The comparisons demonstrate the general utility of the well-known Tanimoto method but also suggest other coefficients that may be worthy of further attention.