It's also great as the core of a programming language. If you can express a feature just in terms of the λ-calculus, you can implement it almost for free. It's just desugaring. Most of Haskell is like this: while the surface language has become rather complex, the majority of the features boil away rather transparently into typed lambda terms. Haskell uses a variant of System F which it actually calls "Core" to underscore how core this concept is :).
Of course, as the accepted answer points out, the λ-calculus is also very useful for logic. In some sense, it is a sort of "proof essence": the basic building block of what a proof is. I really like this notion because it gives me a concrete, first-class object to represent a proof. Seeing proofs as programs really helped me come to terms (heh) with mathematical logic.
One surprising use for the λ-calculus outside of CS is in linguistics. In particular, linguists use typed λ-calculi to construct formal semantics for sentences. It's a way to build up the meaning of, well, meaning. Or at least the things we say ;). I'm not super familiar with semantics in linguistics, but I've always thought it was very cool that they also use some of the same tools as programming language theory! Wikipedia has more about this: http://en.wikipedia.org/wiki/Formal_semantics_%28linguistics...