I've used them (though more generally a directed acyclic graph) when doing certain kinds of analysis of code execution paths (working in embedded software). They do tend to show up in UI work as well (in an ad-hoc, implicit fashion), in my experience, though generally when you're looking at something across the whole UI as opposed to implementing a specific element of it. I've also used them in a somewhat ad-hoc build-system like utility as well.
(And to be clear, none of these involve sitting down and writing some generic Tree<T> structure, they're all cases of "Well, there's some tree-like datastructure that already exists or is a natural fit for this system and I'm going to be traversing it depth-first or breadth-first to do something to the elements of it or calculate something based on what nodes I pass through on a given traversal")
(And to be clear, none of these involve sitting down and writing some generic Tree<T> structure, they're all cases of "Well, there's some tree-like datastructure that already exists or is a natural fit for this system and I'm going to be traversing it depth-first or breadth-first to do something to the elements of it or calculate something based on what nodes I pass through on a given traversal")