  Maximum Principles on unbounded domains play a crucial r\^ole in several
problems related to linear second-order PDEs of elliptic and parabolic type. In
this paper we consider a class of sub-elliptic operators $\mathcal{L}$ in
$\mathbb{R}^N$ and we establish some criteria for an unbounded open set to be a
Maximum Principle set for $\mathcal{L}$. We extend some classical results
related to the Laplacian (by Deny, Hayman and Kennedy) and to the
sub-Laplacians on stratified Lie groups (by Bonfiglioli and the second-named
author).
