Category theory is mostly useful if you're getting very deep into Haskell, or if—for some reason—you need to generalize the lamba calculus to handle strange new kinds of computations.

In particular, the lamba calculus is closely related to Cartesian closed categories, which are in turn related to topoi (which are used in many cases of mathematical logic). And from there it's a small leap to probability and generalizations of probability theory.

So basically, if you're a programming language designer with esoteric tastes, category theory contains some great abstractions.

Here's​ an example showing how to represent quantum superposition as a monad: http://blog.sigfpe.com/2007/02/monads-for-vector-spaces-prob... If this kind of thing makes you drool, go learn some category theory. :-)