If you're in a heavily concurrent environment, then pure functional programming is useful. The lack of mutable state makes concurrency almost trivial. See Erlang.
In a multiparadigm language, you may want to model some things functionally if the existence of mutable state is must an implementation detail, and thus FP is a good model for the problem domain. For example, see list comprehensions in Python or std.range in the D programming language. These are inspired by functional programming.