Clustered regularly interspaced short palindromic repeats (CRISPR) machineries are prokaryotic immune systems that have been adapted as versatile gene editing and manipulation tools. We found that CRISPR nucleases from two families, Cpf1 (also known as Cas12a) and Cas9, exhibit differential guide RNA (gRNA) sequence requirements for cleavage of the two strands of target DNA in vitro. As a consequence of the differential gRNA requirements, both Cas9 and Cpf1 enzymes can exhibit potent nickase activities on an extensive class of mismatched double-stranded DNA (dsDNA) targets. These properties allow the production of efficient nickases for a chosen dsDNA target sequence, without modification of the nuclease protein, using gRNAs with a variety of patterns of mismatch to the intended DNA target. In parallel to the nicking activities observed with purified Cas9 in vitro, we observed sequence-dependent nicking for both perfectly matched and partially mismatched target sequences in a Saccharomyces cerevisiae system. Our findings have implications for CRISPR spacer acquisition, off-target potential of CRISPR gene editing/manipulation, and tool development using homology-directed nicking.