EXPSPACE-complete problems I am currently trying to find EXPSPACE-complete problems 
(mainly to find inspiration for a reduction), and 
I am surprised by the small number of results coming up.

So far, I found these, and I have trouble expanding the list:


universality (or other properties) of regular expressions with exponentiation.
problems related to vector addition systems
unobservable games (see for instance this blog)
some fragment of FO-LTL, in On the Computational Complexity of Decidable Fragments of First-Order-Linear Temporal Logics


Do you know other contexts when EXPSPACE-completeness appears naturally?
Extending the example pointed out by Emil Jerabek in the comments, $\mathsf{EXPSPACE}$-complete problems arise naturally all over algebraic geometry. This started (I think) with the Ideal Membership Problem (Mayr&ndash;Meyer and Mayr) and hence the computation of Gr&ouml;bner bases. This was then extended to the computation of syzygies (Bayer and Stillman). Many natural problems in computational algebraic geometry end up being equivalent to one of these problems. Also see the Bayer&ndash;Mumford survey "What can be computed in algebraic geometry?"