"Functional programming" is one of those terms that's so undefined (and, really, indefinable) that it basically boils down to "I'll define it to mean that what I'm doing fits and what you're doing doesn't".
I think most "functional programmers" will agree on this definition: avoid (side) effects, or at least try to isolate them from the rest of your program.
It doesn't mention functions at all, which can confuse programmers unfamiliar with Lisp, ML, or Haskell. However, when you actually program with such restrictions, your only choice is closures or insanity.
"Most" functional programmers might agree that is a component, but that it is missing many other critical elements of a useful definition. Immutability is a recent one, for instance.
Then you get people like me who observe there really are two "functional"s: There's an old one that simply means functions are first-class objects and usually means you get closures. This is the definition whereby Lisp is the canonical functional language. Then there's the more modern definition that involves immutable variables, no side effects or carefully-isolated side-effects, all of the older definition's closures and such, and possibly a few other things depending on who you talk to. Note by this definition Lisp is no longer "functional".
C being C, it can do the older functional style with some manually-hacked-in closures, at which point you can squint and call it an old-style-functional language. Certainly more so than a Basic with no ability to have a function pointer at all, though lacking closure support. (Note I say "a Basic", I know some can and some can't.) No way is it a new-style functional language, and it never will be. (Modulo http://conal.net/blog/posts/the-c-language-is-purely-functio... , of course.)
Side point: I wasn't talking about programming languages. I was talking about programming styles.
Then by my definition (which I no longer consider universal), programming in a functional style drives you crazy unless you can use functions as first class entities.