Closed set on Euclidean space that is not compact

Being closed means nothing but being the complement of an open set. So take any bounded open subset $S \subset \mathbb R^n$, then $\mathbb R^n \setminus S$ is closed but not bounded. What you are looking for.

I.e:, Any complement of any open ball!

A simple example of a closed but unbounded set is $[0,\infty)$.