We had been shipping products along similar lines written in C# (e.g. this) but we also had a strong background in the commercial use of OCaml. We were enthusiastic early adopters of F# when it was still a research prototype back in 2006 because we recognised the potential of having a decent modern OCaml-like language on the industrial-strength .NET platform and, consequently, we pushed to have it productized. The result has been an incredible success and F# has far exceeded our lofty expectations.
For us, F# has many different advantages and we use it for a wide variety of applications. We have hundreds of thousands of lines of F# code in production. We now use F# for all of our LOB apps: our credit card transactions are processed using F# code, our product notifications are sent using F# code, our subscriptions are handled using F# code, our accounts are done using F# code and so on. Perhaps the main language feature that pays dividends here is pattern matching. We even used F# to color syntax highlight our latest book...
Our visualization library is a big seller and its functionality centers on F# interactive running in Visual Studio. Our library augments this with the ability to spawn interactive 2D and 3D visualizations with minimal effort (e.g. just Plot([Function sin], (-6., 6.)) to plot a sine wave). In particular, all threading issues are completely automated so users do not have to worry about UI threads and dispatch. First-class functions and laziness were extremely valuable when writing this part of the library and algebraic datatypes were used extensively elsewhere. Predictable performance also proved to be valuable here when our customers hit performance bugs in WPF's hit testing and were easily able to reimplement the relevant code in F# for a 10,000× performance improvement. Due to the free-form nature of this product's GUI, the GUI designer and C# would not have been beneficial.
Much of our work revolves around numerical methods, including both our commercial libraries and books. F# is much stronger in this area than C# because it offers high-level abstractions (e.g. higher-order functions) with minimal performance penalties. Our most compelling result in this context was the creation of a simple but generalized implementation of QR decomposition from linear algebra that was 20× shorter than the Fortran code from the reference implementation of LAPACK, up to 3× faster than the vendor-tuned Intel Math Kernel Library and more generic because our code can handle matrices of any type, even symbolic matrices!
We are currently developing WPF/Silverlight components in a mix of F# (for the guts) and C# (for the shim), building WPF apps to act as interactive manuals for our software products and I am writing a new book, Multicore F#, that will be the definitive guide to shared-memory parallel programming on .NET.