Why do I find Category Theory mostly just a way to make simple things difficult? I have a basic working knowledge of category thoery since I do research in programming languages and typed lambda-calculus.  Indeed, I have refereed many papers in my area based on category theory.
But, in doing this refereeing, and in reading many important categorial papers in my area, I simply find the terminology and presentation style extremely opaque compared to style that I prefer which instead emphasizes logic inference rules and extensions of the lambda calculus.
Given the (extended) Curry-Howard Isomorphism between programming languages, logics, and categories, it's clear that I can understand the concepts I need by mapping category theory into the other two.  But, am I missing something in the process, or are the papers I'm refereeing just making things more difficult than they need to be? 
 A: Although to you, category theory is merely an inefficient framework for data about logic and programming languages, to mathematicians working in areas like algebraic geometry and algebraic topology, categories are truly essential.  For us, some of our most basic notions make no sense and look extremely awkward (in fact, some of them are from pre-category days, and no one really knew what we wanted intuitively until after we started using categories) until you phrase them in terms of categories and universal properties of objects and morphisms (and 2-morphisms, etc).  Additionally, it helps us tell what various types of mathematical objects have in common, and how they relate via functors and natural transformations.
As far as recasting algebraic topology and algebraic geometry in terms of lambda calculus, I'd rather like to see that if anyone can manage to, say, give an alternative definition of stack or gerbe or model structure which are more intuitive without using categories and groupoids and the like.
A: As a topologist/category theorist with an interest in type systems I can assure you that I find pages full of sequents hard to understand :)
Actually I think the approaches are complementary.  Suppose I wanted to talk about the simply-typed lambda calculus (with base types B) and its semantics.  Category theory gives you a very simple definition: we take the free closed cartesian category C on the set B; if I choose interpretations of the types as sets, I get the semantics as the functor from C to Set induced from the map B -> Set and the fact that Set is a CCC.  In the traditional presentation of the STLC, I have to define


*

*the syntax of types

*well-formedness and typing rules for terms

*reduction rules to put terms in normal form

*how to interpret a terms as a function on a set


All told it probably takes a few pages.  (As an aside, it's also not clear what kind of mathematical object is being described, which I think can be a little off-putting to non-logicians.)
Of course the traditional presentation has one big advantage: it tells us what the objects and morphisms of C actually are!  But this is a computation which we could (and presumably would) do if we adopted the category-theoretic definition of C.  The category approach explains why we wrote down those few pages of syntax/typing/reduction rules rather than slightly different ones.
Naturally in other parts of mathematics it's common to have objects determined by universal properties (as the free CCC was here) and to want to compute more explicit presentation of them.  If those objects are sufficiently similar to CCCs, then techniques from lambda-calculus may be useful.
A: I think the other answers miss one aspect of this question.  Mathematicians vary in how they do math. Some are "syntactic thinkers" (maybe you), some are "conceptual", and some are "geometric" in the way they think.  That is the way Leone Burton's book Mathematicians as Enquirers: Learning about Learning Mathematics., Kluwer, 2004, analyzes it.  Others take geometric and conceptual to be variations of the same category, and different names are used for the categories, too.  
People are different, and in how they think about abstract ideas they are different in a very deep way.  That is my own experience in both my research career in and teaching.  I took logic from Joe Shoenfield (which gives me a respectable background!) and did work in abstract algebra and then discovered category theory and thought: Way to go!  That is because I think primarily conceptually.
Mike Barr said that to a person with a hammer, everything looks like a nail.  I keep translating problems into categorical language.  You go the other way.  These differences run deep, and should be taken into account when reading other people's stuff.
A: I think for mathematicians, especially the algebraic geometers, category theory has a somewhat different meaning that in your area.
For us, it's primarily an important and quite straightforward way to formalize important properties of natural things, like vector spaces or derived categories or whatever.
In this way category theory is not much different from other subjects, e.g. group theory studies groups. Category theory studies categories. There are some hard to read books on group theory. There are some hard to read books on category theory. Lots of articles about group theory seem to be hard and don't appear to give any benefit to outsider. Same about category theory.
If you search for it, there are really good introductions to the subject. MO already had some questions with links.
