  Motivated by the interpretation of the recent results on the TeV gamma
radiation from the Galactic center, including the new 2004 HESS data, as a
by-product of dark matter particles annihilations, we address the question of
the largest possible neutralino masses and pair annihilation cross sections in
supersymmetric models. Extending the parameter space of minimal models, such as
the mSUGRA and the mAMSB scenarios, to general soft SUSY breaking Higgs masses
gives access to the largest possible pair annihilation rates, corresponding to
resonantly annihilating neutralinos with maximal gaugino-higgsino mixing.
Adopting a model-independent approach, we provide analytical and numerical
upper limits for the neutralino pair annihilation cross section. A possible
loophole is given by the occurrence of non-perturbative electro-weak
resonances, a case we also consider here. We then show that a thorough
inclusion of QCD effects in gluino (co-)annihilations can, in extreme
scenarios, make neutralinos with masses in the hundreds of TeV range, well
beyond the s-wave unitarity bound, viable dark matter candidates. Finally, we
outline the ranges of neutralino masses and cross sections for models thermally
producing a WMAP relic abundance, thus providing reference values for
``best-case'' indirect SUSY dark matter detection rates.
