Functional languages are the current of programming. If you agree on a combination of the following few things as being what you mean when you say "functional programming":
then most of the languages people use -- C++ (C++11 at least, now that it has anonymous functions), Javascript, C#, Python, Ruby, any Lisp, Perl -- support functional programming to a reasonable degree, with the notable exception of Java. (But there are lots of other cool new JVM languages like Scala, Duby and Clojure.)
The same languages often support imperative programming too, but I think that's a feature, not a bug. There will always be some hobbyists who just want to hack together something without learning very much about programming.
I guess a better question is maybe "is functional programming the future of programmers?" In which case I think the answer is yes; it seems like FP is getting more and more mindshare among good programmers and in college curricula.
Because I have been learning about Type Theory, I have become much more aware of and interested in Functional Programming.
If you are unfamiliar with functional programming, Real World Haskell describes functional programming like this:
Because of this functional languages have a number of interesting differences with traditional programming. In functional programming: