Microsoft's recent decision to make F# one of its mainstream programming languages for Visual Studio will increase the acceptance of modern functional programming languages for ordinary industrial development. In the mean time, it is interesting to see where functional programming languages are already being used in industry.
Flying Frog Consultancy are a consultancy, book and software company specializing in the ML family of languages, primarily OCaml and F#. We have product lines including books and on-line magazines teaching OCaml and F# as well as software written in or for these languages.
Microsoft have a considerable investment in the CAML family of functional programming languages. Specifically the OCaml language and Microsoft's own CAML-derivative for .NET called F#. Microsoft's driver verification software is written in OCaml. Microsoft trust the $2bn advertising market on MSN Live to F# code. Microsoft's XBox group write F# programs to analyze the statistics of on-line XBox Live players. Many Microsoft Research projects are written in OCaml and F#, such as the Stochastic Pi Machine (SPiM).
XenSource's value-add over the free edition of Xen is largely a distributed, cross-platform, multi-programming-language management tool stack written in OCaml. XenSource recently sold to Citrix for $500M.
Jane St. Capital have over 20 functional programmers working in offices around the world on finance using OCaml. They recently expanded with a new office in London. Several other financial houses use functional programming languages extensively. Outside ML, Haskell is also popular in the financial sector following a seminal paper by Simon Peyton-Jones.
LexiFi use OCaml extensively for the modeling of financial products (swaps, options etc). Their solution includes software for modeling the life cycle of a product, as well as pricing them. It is closely related to the solution described in the paper by Jean-Marc Eber and Simon Peyton-Jones.Dassault Systemes sell a computer-aided manufacturing environment called Delmia that contains a domain-specific language implemented in OCaml called CellControl for programming assembly-line automata and robots.
Astree is a static analyzer to remove large classes of important bugs from mission critical code used by Airbus.
Credit Suisse First Boston use Haskell in finance.
Linspire is a commercial Linux distribution written partly in Haskell.