We perform a generalized analysis of data from WIMP search experiments for pointlike WIMPs of arbitrary spin and general Lorenz-invariant WIMP-nucleus interaction. We explicitly show that in the nonrelativistic limit only spin-independent (SI) and spin-dependent (SD) WIMP-nucleon interactions survive, which can be parametrized by only five independent parameters. We explore this five-dimensional parameter space to determine whether the annual modulation observed in the DAMA experiment can be consistent with all other experiments which reported null results. The pure SI interaction is ruled out except for a very small region of parameter space with the WIMP mass close to 50 GeV and the ratio of the WIMP-neutron to WIMP-proton SI couplings –0.77<=fn/fp<=–0.75. For the predominantly SD interaction, we find an upper limit on the WIMP mass of about 18 GeV, which can only be weakened if the constraint stemming from null searches for energetic neutrinos from WIMP annihilation the Sun is evaded. None of the regions of the parameter space that can reconcile all WIMP search results can be easily accommodated in the minimal supersymmetric standard model.