  We discuss a formalism for the spin correlations and polarizations in
two-particle systems with spins half-half, half-one and one-one, and provide
the connections between the polarizations and correlations with the joint
angular distributions of decay products identifying the asymmetries for them.
We demonstrate the formalism in the processes $e^-e^+\to t\bar{t}$, $gb \to
tW^-$ and $e^-e^+\to ZZ$ in the standard model as examples. We investigate the
effect of some anomalous couplings on the polarizations and spin correlations
in the processes $e^-e^+\to t\bar{t}$, $gb \to tW^-$ and $u\bar{d}\to ZW^+$ at
parton level and compare their strengths. The spin correlations have the
potential to provide a significant improvement over the polarizations in
probing the anomalous couplings.
