Hacker News Reader

Fixed point operators are heavily used in abstract interpretation (https://secure.wikimedia.org/wikipedia/en/wiki/Abstract_inte...), which in turn is used in static analysis of programs for automatic bug detection or compiler optimizations. In certain situations it can also be used to formally prove the correctness of a program. Just to give a concrete example, this is a static analyzer based on abstract interpretation: http://www.astree.ens.fr/ . Polyspace (https://secure.wikimedia.org/wikipedia/en/wiki/Polyspace) is another static analysis tool that uses abstract interpretation.

I think Haskell uses a fixpoint combinator built into the core language under some syntactic sugar to enable any sort of recursion, so the real-world use would be pretty much making every Haskell program ever work.

Neither have I. I just find it very beautiful.