  We perform a systematic study of the multi-wavelength signal induced by
weakly interacting massive particle (WIMP) annihilations at the Galactic Center
(GC). Referring to a generic WIMP dark matter (DM) scenario and depending on
astrophysical inputs, we discuss spectral and angular features and sketch
correlations among signals in the different energy bands. None of the
components which have been associated to the GC source Sgr A*, nor the diffuse
emission components from the GC region, have spectral or angular features
typical of a DM source. Still, data-sets at all energy bands, namely, the
radio, near infrared, X-ray and gamma-ray bands, contribute to place
significant constraints on the WIMP parameter space. In general, the gamma-ray
energy range is not the one with the largest signal to background ratio. In the
case of large magnetic fields close to the GC, X-ray data give the tightest
bounds. The emission in the radio-band, which is less model dependent, is very
constraining as well. The recent detection by HESS of a GC gamma-ray source,
and of a diffuse gamma-ray component, limits the possibility of a DM discovery
with next generation of gamma-ray telescopes, like GLAST and CTA. We find that
the most of the region in the parameter space accessible to these instruments
is actually already excluded at other wave-lenghts. On the other hand, there
may be still an open window to improve constraints with wide-field radio
observations.
