  We obtain infinite classes of new Einstein-Sasaki metrics on complete and
non-singular manifolds. They arise, after Euclideanisation, from BPS limits of
the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces
L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1)
isometry group. They are topologically S^2 x S^3. Their AdS/CFT duals will
describe quiver theories on the four-dimensional boundary of AdS_5. We also
obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions
D=2n+1 \ge 5, with U(1)^{n+1} isometry.
