Experimental detection of RNA splicing branchpoints is difficult. To date, high-confidence experimental annotations exist for 18% of 3′ splice sites in the human genome. We develop a deep-learning-based branchpoint predictor, LaBranchoR, which predicts a correct branchpoint for at least 75% of 3′ splice sites genome-wide. Detailed analysis of cases in which our predicted branchpoint deviates from experimental data suggests a correct branchpoint is predicted in over 90% of cases. We use our predicted branchpoints to identify a novel sequence element upstream of branchpoints consistent with extended U2 snRNA base-pairing, show an association between weak branchpoints and alternative splicing, and explore the effects of genetic variants on branchpoints. We provide genome-wide branchpoint annotations and in silico mutagenesis scores at http://bejerano.stanford.edu/labranchor.