  We prove several results of the following general form: automorphisms of (or
actions of ${\mathbb{Z}}^d$ on) certain kinds of simple separable unital
C*-algebras $A$ which have a suitable version of the Rokhlin property are
generic among all automorphisms (or actions), or in a suitable class of
automorphisms. That is, the ones with the version of the Rokhlin property
contain a dense $G_{\delta}$-subset of the set of all such automorphisms (or
actions).
  Specifically, we prove the following. If $A$ is stable under tensoring with
the Jiang-Su algebra $Z,$ and has tracial rank zero, then automorphisms with
the tracial Rokhlin property are generic. If $A$ has tracial rank zero, or,
more generally, $A$ is tracially approximately divisible together with a
technical condition, then automorphisms with the tracial Rokhlin property are
generic among the approximately inner automorphisms. If $A$ is stable under
tensoring with the Cuntz algebra ${\mathcal{O}}_{\infty}$ or with a UHF algebra
of infinite type, then actions of ${\mathbb{Z}}^d$ on $A$ with the Rokhlin
property are generic among all actions of ${\mathbb{Z}}^d.$ We further give a
related but more restricted result for actions of finite groups.
