These are probably the most important places, besides FP, where categories are used in computer science, but there are others: logic programming, computer graphics and vision, knowledge representation, ontology, &c. The applications to FP are most visible because (i) Haskell monads are a little slice of category theory, so users as well as language designers need to get their hands dirty[+], and (ii) it's very natural to want a realisation of a categorical semantics to have first-class functions, ideally lazy functions, because that makes the realisation easier.
[+] Categorical abstractions in semantics are dirty, don't let people fool you into believing they are pure and clean.
Other areas of CS where category theory is applied:
1. Algebraic data types and modules. E.g., http://reperiendi.wordpress.com/2007/11/03/category-theory-f...
2. Semantics of non-terminating programs. E.g., http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.2...
3. Semantics of concurrency. E.g., http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.8...
These are probably the most important places, besides FP, where categories are used in computer science, but there are others: logic programming, computer graphics and vision, knowledge representation, ontology, &c. The applications to FP are most visible because (i) Haskell monads are a little slice of category theory, so users as well as language designers need to get their hands dirty[+], and (ii) it's very natural to want a realisation of a categorical semantics to have first-class functions, ideally lazy functions, because that makes the realisation easier.
[+] Categorical abstractions in semantics are dirty, don't let people fool you into believing they are pure and clean.