  In experiments for direct dark matter searches, neutrinos coherently
scattering off nuclei can produce similar events as Weakly Interacting Massive
Particles (WIMPs). The calculated count rate for solar neutrinos in such
experiments is a few events per ton-year. This count rate strongly depends on
the nuclear recoil energy threshold achieved in the experiments for the WIMP
search. We show that solar neutrinos can be a serious background source for
direct dark matter search experiments using Ge, Ar, Xe and CaWO_4 as target
materials. To reach sensitivities better than approximatly 10^-10 pb for the
elastic WIMP nucleon spin-independent cross section in the zero-background
limit, energy thresholds for nuclear recoils should be approximatly >2.05 keV
for CaWO_4, >4.91 keV for Ge, >2.89 keV for Xe, and >8.62 keV for Ar as target
material. Next-generation experiments should not only strive for a reduction of
the present energy thresholds but mainly focus on an increase of the target
mass. Atmospheric neutrinos limit the achievable sensitivity for the
background-free direct dark matter search to approximatly >10^-12 pb.
