I can think of several additions to your list which don't seem to be represented yet.
This first example is rather general, but afterward I will discuss how it is used in Springer theory. First, suppose that $f:X \to Y$ is a proper map of stratified irreducible complex algebraic varieties such that, if $Y = \cup Y_n$ is the stratification of $Y,$ the restriction of $f$ to $f^{-1}(Y_n) \to Y_n$ is topologically locally trivial (there's a theorem (not sure who it's by) that says we can always find a stratification such that this condition holds). Furthermore, we say that $f$ is semi-small if for each stratum $Y_n,$ twice the dimension of the fiber of $f^{-1}(Y_n) \to Y_n$ is less than or equal to the codimension of $Y_n$ inside $Y.$ This condition is important largely because the pushforward of a perverse sheaf under a semismall map is still perverse. Furthermore, we say that a stratum $Y_n$ is relevant whenever equality holds above, i.e., twice the fiber dimension is equal to the codimension. These will be important soon, as they will be the subvarieties appearing in the decomposition theorem.
By the assumptions we made on $f:X \to Y,$ we have a monodromy action of $\pi_1(Y_n)$ on the top dimensional cohomology group of the fiber of $f^{-1}(Y_n) \to Y_n.$ This corresponds to a local system $L_{Y_n},$ which we can decompose into irreducible components: $L_{Y_n} = \oplus L_{\rho}^{d_{\rho}}$ where $\rho$ runs over the set of irreducible representations of $\pi_1(Y_n)$ and $d_{\rho}$ are non-negative integers. We then say that a pair $(Y_n, \rho)$ is relevant if $Y_n$ is a relevant stratum and $d_{\rho} \neq 0$ (i.e., $\rho$ appears in the decomposition of the representation of $\pi_1(Y_n)$).
Now we can finally state a theorem, which I believe is due to Borho and Macpherson, but perhaps others deserve credit as well. Keep the initial assumptions on $f:X \to Y,$ but now assume in addition that $X$ is smooth. Then a little work plus the decomposition theorem says that $f_{\ast}IC_X = \oplus IC_{Z_n}(L_{\rho})^{d_{\rho}}$ where $Z_n$ is the closure of $Y_n$ and the sum ranges over all relevant pairs $(Y_n, \rho).$
This theorem is used in Springer theory (and perhaps other places as well). In this case, we want $f:X \to Y$ to be the Springer resolution. That is, $Y = \mathcal{N},$ the nilpotent cone of a Lie algebra $g$ associated to a reductive group $G$, and $Y = \widetilde{\mathcal{N}},$ the variety of pairs $(x,b)$ where $x \in \mathcal{N},$ $b$ is a Borel subalgebra, and $x \in b.$ If we stratify $\mathcal{N}$ using the $Ad(G)$-orbits (of which there are finitely many), then it turns out that the Springer resolution is semismall and every stratum is relevant. It can furthermore be shown that the $L_{\rho}$ appearing in the theorem above correspond to the irreducible components of the regular representation of the Weyl group of $G.$ This can be seen as follows. There's an analog of the Springer resolution $\pi:\widetilde{g} \to g$ defined as above but with g in place of $\mathcal{N}.$ By proper base change, the pushforward of the constant sheaf on $\widetilde{\mathcal{N}}$ coincides with the pull-back (under the inclusion $\mathcal{N} \to g$) of the pushforward of the constant sheaf on $\widetilde{g}.$ Finally, since $\pi$ is what's known as a small map, the pushforward of the constant sheaf on $\widetilde{g}$ is equal to $IC_g(L)$ where $L$ is the local system on the dense open subset $g^{rs}$ of regular semisimple elements obtained from the $W$-torsor $\widetilde{g^{rs}} \to g^{rs}.$ From all this we obtain that the top-dimensional cohomology groups of Springer fibers produce all irreducible representations of $W.$
In a different direction, let me mention how the decomposition theorem is used in the geometric Satake correspondence (see the Mirkovic-Vilonen paper or the Ginzburg paper on this topic). Geometric Satake is concerned with proving a tensor equivalence between the category of spherical perverse sheaves on the affine Grassmannian (i.e., perverse sheaves which are direct sums of IC sheaves) assoicated to a reductive group $G$ and the category of representations of the Langlands dual of $G.$ This is done through the Tannakian formalism, which in particular requires a tensor structure on spherical perverse sheaves. This tensor structure comes from a convolution product on perverse sheaves, meaning that it comes from a pull-back followed by a tensor product followed by a pushforward. In order to ensure that this operation takes spherical perverse sheaves to spherical perverse sheaves, we need the decomposition theorem.