Accurate pre-mRNA splicing is crucial for gene expression. The 5' splice site (5' ss)--the highly diverse element at the 5' end of introns--is initially recognized via base-pairing to the 5' end of the U1 small nuclear RNA (snRNA). However, many natural 5' ss have a poor match to the consensus sequence, and are predicted to be weak. Using genetic suppression experiments in human cells, we demonstrate that some atypical 5' ss are actually efficiently recognized by U1, in an alternative base-pairing register that is shifted by one nucleotide. These atypical 5' ss are phylogenetically widespread, and many of them are conserved. Moreover, shifted base-pairing provides an explanation for the effect of a 5' ss mutation associated with pontocerebellar hypoplasia. The unexpected flexibility in 5' ss-U1 base-pairing challenges an established paradigm and has broad implications for splice-site prediction algorithms and gene-annotation efforts in genome projects.