I'd like to think that Godel himself would have approved of this particular award, given the mind-bending nature of the Razborov-Rudich result. To use Scott Aaronson's loose formulation, their result can be summarized as
The reason P != NP is so difficult to prove is that P != NPComputational Complexity (is it the Lance-blog, or the Bill-blog, or a Lance-post in the Bill-blog, or a Lance-post in the Bill-blog-that-used-to-be-Lance's-blog?), and In Theory have detailed explanations of the RR result, and do a far better job than I can do here.
To put it in perspective, the Razborov-Rudich result is a "meta-result": it says that no proofs of a certain kind (the so-called natural proofs) can be used to prove P != NP, unless other hardness assumptions break to begin with. Another example of a meta-result is the (older) result by Baker, Gill and Solovay that the P=NP question does not relativize (i.e cannot be proved using methods that hold under the application of oracles).
Razborov-Rudich really put a shaft in methods for separating P and NP (see this pessimistic post by Lance). If only all the P vs NP cranks actually tried examining proofs like this before wasting all those valuable bits on comp.theory ;)
(HT: [LB, UB] and Process Algebra Diary).