  We study the direct detection of supersymmetric dark matter in the light of
recent experimental results. In particular, we show that regions in the
parameter space of several scenarios with a neutralino-nucleon cross section of
the order of $10^{-6}$ pb, i.e., where current dark matter detectors are
sensitive, can be obtained. These are supergravity scenarios with intermediate
unification scale, and superstring scenarios with D-branes.
