We study the spin-dependent WIMP scattering off nuclei for a variety of targets of experimental interest. In evaluating the spin structure functions, we have included the recently proposed leading long-range two-body currents in the most important isovector contribution. We show, however, that such effects are essentially independent of the target nucleus and, as a result, they can be treated as a mere renormalization of the effective nucleon cross-section or, equivalently, of the corresponding effective coupling, with reduction factors around 25%. Using these effects in the spin structure functions, we compute the relevant event rates due to the spin for various targets of experimental interest.