Examples of non linear partial order relations

Question

Apart from $\subseteq$, what are examples of nonlinear partial order relations?

Answer 1

In $\mathbb N$, consider that relation $a\mid b$, for instance.

Answer 2

Take a $T_0$ space $X$ (not $T_1$, to avoid boring cases) and define $x \le y$ iff $x \in \overline{\{y\}}$, for $x,y \in X$.