Using a simplified model framework, we assess observational limits and discovery prospects for neutralino dark matter, taken here to be a general admixture of bino, wino, and Higgsino. Experimental constraints can be weakened or even nullified in regions of parameter space near 1) purity limits, where the dark matter is mostly bino, wino, or Higgsino, or 2) blind spots, where the relevant couplings of dark matter to the Z or Higgs bosons vanish identically. We analytically identify all blind spots relevant to spin-independent and spin-dependent scattering and show that they arise for diverse choices of relative signs among M_1, M_2, and μ. At present, XENON100 and IceCube still permit large swaths of viable parameter space, including the well-tempered neutralino. On the other hand, upcoming experiments should have sufficient reach to discover dark matter in much of the remaining parameter space. Our results are broadly applicable, and account for a variety of thermal and non-thermal cosmological histories, including scenarios in which neutralinos are just a component of the observed dark matter today. Because this analysis is indifferent to the fine-tuning of electroweak symmetry breaking, our findings also hold for many models of neutralino dark matter in the MSSM, NMSSM, and Split Supersymmetry. We have identified parameter regions at low tan β which sit in a double blind spot for both spin-independent and spin-dependent scattering. Interestingly, these low tan β regions are independently favored in the NMSSM and models of Split Supersymmetry which accommodate a Higgs mass near 125 GeV.