  We compute the complexity of two infinite families of finite graphs: the
Sierpi\'{n}ski graphs, which are finite approximations of the well-known
Sierpi\'nsky gasket, and the Schreier graphs of the Hanoi Towers group
$H^{(3)}$ acting on the rooted ternary tree. For both of them, we study the
weighted generating functions of the spanning trees, associated with several
natural labellings of the edge sets.
