We examine the interaction between monovalent cations and DNA using several different assays that measure the stability of double-stranded DNA (dsDNA). The thermal melting of dsDNA and the mechanical separation of dsDNA into two single strands both depend on the stability of dsDNA with respect to ssDNA and are sensitive to the interstrand phosphate repulsion. We find that the experimentally measured melting temperatures and unzipping forces are approximately the same for all of the ions considered in this study. Likewise, the force required to transform B-DNA into the overstretched form is also similar for all of the ions. In contrast, for a given ion concentration, the force at which the overstretched state fully relaxes back to the canonical B-DNA form depends on the cation; however, for all cations, the overstretching force decreases with decreasing ion concentration, suggesting that this force is sensitive to screening. We observe a general trend for smaller ions to produce more efficient relaxation. Finally, for a given cation, the relaxation can also depend on the anion.