Let's say that I want to prove that a language is not regular.

The only general technique I know for doing this is the so-called "pumping lemma", which says that if $L$ is a regular language, then there exists some $n>0$ with the following property. If $w$ is a word in $L$ of length at least $n$, then we can write $w=xyz$ (here $x$, $y$, and $z$ are subwords) such that $y$ is nontrivial and $xy^{k}z$ is an element of $L$ for all $k>0$.

This lemma basically reflects the trivial fact that in any directed graph, there is some $n$ such that any path of length at least n contains a loop.

Question: are there any other general techniques for proving that a language is not regular?