Any individual’s genome contains ∼4-5 million genetic variants that differ from reference, and understanding how these variants give rise to trait diversity and disease susceptibility is a central goal of human genetics1. A vast majority (96-99%) of an individual’s variants are common, though at a population level the overwhelming majority of variants are rare2–5. Because of their scarcity in an individual’s genome, rare variants that play important roles in complex traits are likely to have large functional effects6,7. Mutations that cause an exon to be skipped can have severe functional consequences on gene function, and many known disease-causing mutations reduce or eliminate exon recognition8. Here we explore the extent to which rare genetic variation in humans results in near complete loss of exon recognition. We developed a Multiplexed Functional Assay of Splicing using Sort-seq (MFASS) that allows us to measure exon inclusion in thousands of human exons and surrounding intronic sequence simultaneously. We assayed 27,733 extant variants in the Exome Aggregation Consortium (ExAC)9 within or adjacent to 2,339 human exons, and found that 3.8% (1,050) of the variants, almost all of which were extremely rare, led to large-effect defects in exon recognition. Importantly, we find that 83% of these splice-disrupting variants (SDVs) are located outside of canonical splice sites, are distributed evenly across distinct exonic and intronic regions, and are difficult to predict a priori. Our results indicate that loss of exon recognition is an important and underappreciated means by which rare variants exert large functional effects, and that MFASS enables their empirical assessment for splicing defects at scale.