  We study the Tutte polynomial of two infinite families of finite graphs: the
Sierpi\'{n}ski graphs, which are finite approximations of the well-known
Sierpi\'{n}ski gasket, and the Schreier graphs of the Hanoi Towers group
$H^{(3)}$ acting on the rooted ternary tree. For both of them, we recursively
describe the Tutte polynomial and we compute several special evaluations of it,
giving interesting results about the combinatorial structure of these graphs.
