CRISPR-Cas adaptive immune systems protect bacteria and archaea against foreign genetic elements. In Escherichia coli, Cascade (CRISPR-associated complex for antiviral defense) is an RNA-guided surveillance complex that binds foreign DNA and recruits Cas3, a trans-acting nuclease helicase for target degradation. Here, we use single-molecule imaging to visualize Cascade and Cas3 binding to foreign DNA targets. Our analysis reveals two distinct pathways dictated by the presence or absence of a protospacer-adjacent motif (PAM). Binding to a protospacer flanked by a PAM recruits a nuclease-active Cas3 for degradation of short single-stranded regions of target DNA, whereas PAM mutations elicit an alternative pathway that recruits a nuclease-inactive Cas3 through a mechanism that is dependent on the Cas1 and Cas2 proteins. These findings explain how target recognition by Cascade can elicit distinct outcomes and support a model for acquisition of new spacer sequences through a mechanism involving processive, ATP-dependent Cas3 translocation along foreign DNA.