When would you NOT want to use functional programming? What is it not so good at?
I am more looking for disadvantages of the paradigm as a whole, not things like "not widely used", or "no good debugger available". Those answers may be correct as of now, but they deal with FP being a new concept (an unavoidable issue) and not any inherent qualities.
Related:
It's hard for me to think of many downsides to functional programming. Then again, I am a former chair of the International Conference on Functional Programming, so you may safely assume I am biased.
I think the main downsides have to do with isolation and with barriers to entry. Learning to write good functional programs means learning to think differently, and to do it well requires a substantial investment of time and effort. It is difficult to learn without a teacher. These properties lead to some downsides:
It is likely that a functional program written by a newcomer will be unnecessarily slow—more likely than, say, a C program written by a newcomer to C. On the other hand, it is about equally likely that a C++ program written by a newcomer will be unnecessarily slow. (All those shiny features...)
Generally experts have no difficulty writing fast functional programs; and in fact some of the best-performing parallel programs on 8- and 16-core processors are now written in Haskell.
It's more likely that someone starting functional programming will give up before realizing the promised productivity gains than will someone starting, say, Python or Visual Basic. There just isn't as much support in the form of books and development tools.
There are fewer people to talk to. Stackoverflow is a good example; relatively few Haskell programmers visit the site regularly (although part of this is that Haskell programmers have their own lively forums which are much older and better established than Stackoverflow).
It's also true that you can't talk to your neighbor very easily, because functional-programming concepts are harder to teach and harder to learn than the object-oriented concepts behind languages like Smalltalk, Ruby, and C++. And also, the object-oriented community has spent years developing good explanations for what they do, whereas the functional-programming community seem to think that their stuff is obviously great and doesn't require any special metaphors or vocabulary for explanation. (They are wrong. I am still waiting for the first great book Functional Design Patterns.)
A well-known downside of lazy functional programming (applies to Haskell or Clean but not to ML or Scheme or Clojure) is that it is very difficult to predict the time and space costs of evaluating a lazy functional program—even experts can't do it. This problem is fundamental to the paradigm and is not going away. There are excellent tools for discovering time and space behavior post facto, but to use them effectively you have to be expert already.