  We use the results of direct and indirect searches for weakly interacting
massive particles (WIMPs) to obtain bounds on various electro-magnetic form
factors of WIMPs. The limits on the recoil signal in underground dark matter
detection experiments, with standard assumptions about the density and r.m.s.
velocity of WIMPs in the halo, can be translated into the following
model-independent bounds on the magnetic dipole, electric dipole, quadrupole
and anapole moments and the polarizability of WIMPs: mu/mu_n < 1.4 10^{-4}, d <
5 10^{-21}e cm, Q < 6 10^{-7}fm^2, a/mu_n < 3 10^{-2} fm, and chi < 5
10^{-8}fm^3 for a WIMP mass of 100 GeV. The limits on fluxes of highly
energetic neutrinos produced in the annihilation of WIMPs in the center of the
earth and the sun lead to somewhat stronger, but more model dependent bounds.
