  We consider SU(2)-equivariant dimensional reduction of Yang-Mills theory on
manifolds of the form $M\times S^3/\Gamma$, where $M$ is a smooth manifold and
$S^3/\Gamma$ is a three-dimensional Sasaki-Einstein orbifold. We obtain new
quiver gauge theories on $M$ whose quiver bundles are based on the affine ADE
Dynkin diagram associated to $\Gamma$. We relate them to those arising through
translationally-invariant dimensional reduction over the associated Calabi-Yau
cones $C(S^3/\Gamma)$ which are based on McKay quivers and ADHM matrix models,
and to those arising through SU(2)-equivariant dimensional reduction over the
leaf spaces of the characteristic foliations of $S^3/\Gamma$ which are K\"ahler
orbifolds of $\mathbb{C} P^1$ whose quiver bundles are based on the unextended
Dynkin diagram corresponding to $\Gamma$. We use Nahm equations to describe the
vacua of SU(2)-equivariant quiver gauge theories on the cones as moduli spaces
of spherically symmetric instantons. We relate them to the Nakajima quiver
varieties which can be realized as Higgs branches of the worldvolume quiver
gauge theories on D$p$-branes probing D$(p+4)$-branes which wrap an ALE space,
and to the moduli spaces of spherically symmetric solutions in putative
non-abelian generalizations of two-dimensional affine Toda field theories.
