Since we've launched F# in Visual Studio 2010, we've often said "use F# for your core logic, and do the GUI with designer tools, generating some C# or Visual Basic". Case after case is arising where people are doing just this - writing AI engines in F# (e.g. Path of Go), or energy industry computation engines in F# (Simon Cousins, see his answer on stackoverflow), or social networking portals where the fundamental algorithms are in F# (Project Emporia).
Now comes a great one. Tabbles is a new way of organizing files: it combines virtual folders and tags, and auto-organizes and tags your files in very intelligent ways. It's been called "what WinFS should have been". But the best part: the developers have revealed that tabbles is written in F# wherever possible.
You can read the whole story of the evolution of tabbles here. There are lots of user stories of using tabbles here. F# programming seems to have really served them well.
Main link: www.tabbles.net
[ Update: the guys from tabbles have left a comment below - it turns out tabbles is pretty much completely in F# :-) ]