  We perform a model-independent classification of Weakly Interacting Massive
Particle (WIMP) dark matter candidates that have the property that their
scattering off nucleons is dominated by spin-dependent interactions. We study
renormalizable theories where the scattering of dark matter is elastic and
arises at tree-level. We show that if the WIMP-nucleon cross section is
dominated by spin-dependent interactions the natural dark matter candidates are
either Majorana fermions or real vector bosons, so that the dark matter
particle is its own anti-particle. In such a scenario, scalar dark matter is
disfavored. Dirac fermion and complex vector boson dark matter are also
disfavored, except for very specific choices of quantum numbers. We further
establish that any such theory must contain either new particles close to the
weak scale with Standard Model quantum numbers, or alternatively, a $Z'$ gauge
boson with mass at or below the TeV scale. In the region of parameter space
that is of interest to current direct detection experiments, these particles
naturally lie in a mass range that is kinematically accessible to the Large
Hadron Collider (LHC).
