For fluid variables, see the withdrawn SRFI 15, <https://srfi.schemers.org/srfi-15/srfi-15.html>.  Dynamic variables are an equivalent Common Lisp concept.  Fluid and dynamic variables behave like global variables that have been bound permanently to a parameter, so they are accessible from everywhere and can be parameterized anywhere.  In Common Lisp, all top-level variables (but not constants or functions) are dynamic, and conventionally are written with an asterisk as a prefix and suffix.  In addition, when a variable in a Common LIsp lambda-list (or equivalent) is dynamic, it will be parameterized rather than lexically bound when the procedure is called.

All the examples I have found (except Marc's, thank you Marc) involve using parameters in exactly this way, which I why I am especially interested in other use cases.

There is a problem with parameters: if a procedure implicitly depends on a parameter, and you want to use the procedure in a "localized" way, then binding the parameter around the whole or a substantial part of a program is convenient.  But to use such a procedure in a "universal" way independent of its context, it is necessary to wrap *every* call in a parameterize expression.

John Cowan          http://vrici.lojban.org/~cowan        cowan@ccil.org
Objective consideration of contemporary phenomena compel the conclusion
that optimum or inadequate performance in the trend of competitive
activities exhibits no tendency to be commensurate with innate capacity,
but that a considerable element of the unpredictable must invariably be
taken into account. --Ecclesiastes 9:11, Orwell/Brown version