Many genetic variations are single nucleotide polymorphisms (SNPs). Non-synonymous SNPs are 'neutral' if the resulting point-mutated protein is not functionally discernible from the wild type and 'non-neutral' otherwise. The ability to identify non-neutral substitutions could significantly aid targeting disease causing detrimental mutations, as well as SNPs that increase the fitness of particular phenotypes. Here, we introduced comprehensive data sets to assess the performance of methods that predict SNP effects. Along we introduced SNAP (screening for non-acceptable polymorphisms), a neural network-based method for the prediction of the functional effects of non-synonymous SNPs. SNAP needs only sequence information as input, but benefits from functional and structural annotations, if available. In a cross-validation test on over 80,000 mutants, SNAP identified 80% of the non-neutral substitutions at 77% accuracy and 76% of the neutral substitutions at 80% accuracy. This constituted an important improvement over other methods; the improvement rose to over ten percentage points for mutants for which existing methods disagreed. Possibly even more importantly SNAP introduced a well-calibrated measure for the reliability of each prediction. This measure will allow users to focus on the most accurate predictions and/or the most severe effects. Available at http://www.rostlab.org/services/SNAP.