  In this paper, we study boundary actions of CAT(0) spaces from a point of
view of topological dynamics and $C^*$-algebras. First, we investigate the
actions of right-angled Coexter groups and right-angled Artin groups with
finite defining graphs on the visual boundaries and the Nevo-Sageev boundaries
of their natural assigned CAT(0) cube complexes. In particular, we establish
(strongly) pure infiniteness results for reduced crossed product $C^*$-algebras
of these actions through investigating the corresponding $\cat$ cube complexes
and establishing necessary dynamical properties such as minimality, topological
freeness and pure infiniteness of the actions. In addition, we study actions of
fundamental groups of graphs of groups on the visual boundaries of their
Bass-Serre trees. We show that the existence of repeatable paths essentially
implies that the action is $2$-filling, from which, we also obtain a large
class of unital Kirchberg algebras. Furthermore, our result also provides a new
method in identifying $C^*$-simple generalized Baumslag-Solitar groups. The
examples of groups obtained from our method have $n$-paradoxical towers in the
sense of \cite{G-G-K-N}. This class particularly contains non-degenerated free
products, Baumslag-Solitar groups and fundamental groups of $n$-circles or
wedge sums of $n$-circles.
