I know of several functional languages - F#, Lisp and its dialects, R, and more. However, as I've never used any of them (although the three I mentioned are on my "to-learn" list), I was wondering about the pros/cons of the various functional languages out there. Are there significant pros/cons, both in learning the language and in any real-world applications of said language?
I'm not sure if your question is to functional languages in general, or differences between them. For general info on why functional:
http://paulspontifications.blogspot.com/2007/08/no-silver-bullet-and-functional.html
Why Functional Programming Matters
As far as differences between functional languages:
Distinctive traits of the functional languages
The awesome thing about functional languages is that base themselves off of the lambda calculus and other math. This results in being able to use similar algorithms and thoughts across languages more easily.
As far as which one you should learn: Pick one that will have a comfortable environment for you. For example, if you're using .NET and Visual Studio, F# is an excellent fit. (Actually, the VS integration makes F# a strong contender, period.) The book "How to Design Programs" (full text, free, online) with PLT Scheme is also a good choice.
I'm biased, but F# looks to have the biggest "real-world" potential. This is mainly because of the nice IDE/.NET integration, allowing you to fully tap .NET and OO, while keeping a lot of functional power (and extending it in ways too). Scala might be possible contender, but it's more of an OO language that has some functional features; hence Scala won't be as big a productivity gain.
Edit: Just to note JavaScript and Ruby, before someone comments on that :). Ruby is something else you could take a look at if you're doing that type of web dev, as it has a lot of functional concepts in, although not as polished as other languages.
The biggest downside is that once you see the power you can have, you won't be happy using lesser languages. This becomes a problem if you're forced to deal with people who haven't yet understood.
One final note, the only "con" is that "it's so complicated". This isn't actually true -- functional languages are often simpler -- but if you have years of C or whatnot in your brain, it can be a significant hurdle to "get" the functional concept. After it clicks, it should be relatively smooth sailing.