  I combine recent results in the structure theory of nuclear C*-algebras and
in topological dynamics to classify certain types of crossed products in terms
of their Elliott invariants. In particular, transformation group C*-algebras
associated to free minimal Z^d-actions on the Cantor set with compact space of
ergodic measures are classified by their ordered K-theory. In fact, the
respective statement holds for finite dimensional compact metrizable spaces,
provided that projections of the crossed products separate tracial states.
Moreover, C*-algebras associated to certain minimal homeomorphisms of odd
dimensional spheres are only determined by their spaces of invariant Borel
probability measures (without a condition on the space of ergodic measures).
Finally, I show that for a large collection of classifiable C*-algebras,
crossed products by Z^d-actions are generically again classifiable.
