The application I like most is programming languages--not just compilers and interpreters but also various tools and analysis. I think quite a lot of software related to languages gets written in functional languages, and in my experience Haskell is much better for that sort of thing than Python or JavaScript. I've actually written very similar interpreters in all three languages so I think I have a particularly useful perspective here.

Another field is web development. There was an article recently about Yesod's being as productive as Rails; I think a functional language would be a safe choice for your next web app.

I think there has even been some 3D modelling software written in a functional language--Wings3D is written in Erlang unless I'm much mistaken.

I haven't really been paying much attention to other fields--all my time recently has been spent almost equally between language stuff and web stuff--but I think there are other cases where functional programming is a fairly safe choice that are not just calculations.

Coincidentally, I doubt that we will see Photoshop or a word processor in a functional language any time soon. Not because functional languages are particularly unsuitable but because word and image processing software is rather big, boring and requires a lot of specialized knowledge; I imagine the intersection between "functional programming enthusiasts" and "word processor enthusiasts" is not very big. In fact, most of the people I know who like functional programming use something like LaTeX rather than a word processor and don't do much image manipulation either.