  In this paper we discuss the excess gamma rays from the Galactic center, the
WMAP haze and the CoGeNT and DAMA results in WIMPless models. At the same time
we also investigate the low energy constraints from the anomalous magnetic
moment of leptons and from some lepton flavor violating decays. It is found
that, for scalar or vector WIMPless dark matter, neither the WMAP haze nor the
CoGeNT and DAMA observations could be explained simultaneously with the excess
gamma rays from the Galactic center. As to fermion WIMPless dark matter, it is
only marginally possible to accommodate the CoGeNT and DAMA results with the
excess gamma rays from the Galactic center with vector connector fields. On the
other hand, only scalar connector fields could interpret the WMAP haze
concerning the constraints of anomalous magnetic moment of leptons.
Furthermore, if there is only one connector field for all the charged leptons,
some lepton flavor violating decays could happen with too large branching
ratios severely violating the experimental bounds.
