  We consider neutralino-proton cross sections for halo dark matter neutralinos
within the framework of supergravity models with R-parity invariance for models
with universal soft breaking (mSUGRA) and models with nonuniversal soft
breaking. The analysis includes the necessary corrections to treat the large
tanbeta region (i.e. L-R mixing in the squark and slepton mass matrices, loop
corrections to the b and tau masses,etc) and includes all coannihilation
phenomena. For mSUGRA, dark matter detectors with current sensitivity are seen
to be probing the region where tanbeta>~25, Omega h^2 <0.1, m_{chi_1^0}~<90
GeV, and for the light Higgs, m_h~< 120 GeV. Nonuniversal models can have a
much larger cross section, and current detectors can probe part of the
parameter space where tan>~4. Minimum cross sections are generally greater than
10^{-9} pb to 10^{-10} pb for m_{1/2} <600 GeV (and hence accessible to planned
future detectors), with the exception of a region when mu <0 where for
m_{1/2}>~450 GeV, 4~< tanbeta~<20, the cross section drops to a minimum of
about 1\times10^{-12} pb at m_{1/2}=600 GeV, tan beta=~10. In this region, the
gluino and squarks lie above 1 TeV, but should still be accessible to the LHC.
