Here is an example of an easy corollary of the Hales-Jewett theorem:

**Theorem:** For every finite topological space $X$ and $r \in \mathbb{N}$, there is a finite topological space $Y$ such that if $Y$ is $r$-colored, then we can find a monochromatic copy of $X$.

**Proof:** Using the Hales-Jewett theorem, pick $n$ large enough so that any $r$-coloring of $X^n$ provides a monochromatic combinatorial line. Then set $Y = X^n$ (with the usual product topology), and observe that every combinatorial line in $X^n$ is homeomorphic to $X$.

This type of result fits into the area called *induced Ramsey theory*. The Hales-Jewett theorem gives us many such results: the same proof works for finite metric spaces (use the sup metric on the product), graphs (use the strong product), digraphs (use a suitable generalization of the strong product), and more. It works for finite groups too, provided you are willing to weaken the conclusion a bit:

**Theorem:** For every finite group $G$ and $r \in \mathbb{N}$, there is a finite group $H$ such that if $H$ is $r$-colored, then we can find a subgroup $G'$ of $H$ isomorphic to $G$ and an element $h \in H$ such that $hG$ is monochromatic.

**Proof:** Essentially the same: just observe that in $G^n$, combinatorial lines are shifted copies of $G$.

Of course, many results from induced Ramsey theory involve coloring not points, but pairs of points, triples of points, etc. These kinds of results do not seem to follow easily from the Hales-Jewett theorem.

In addition to these kinds of results, the Hales-Jewett theorem is used in the proof of the Graham-Leeb-Rothschild theorem, the edge-induced graph theorem, and its bipartite version (these are in sections 2.4, 5.2, and 5.3 of the Graham-Rothschild-Spencer book). It also gives quick proofs for van der Waerden's theorem and its higher-dimensional analogue, Gallai's theorem. See also Exercise 15 of this blog post of Terry Tao for further examples of what you can do using the Hales Jewett theorem.