Can one automate algorithmic analysis?
Implicit Complexity has taught us that (some) complexity classes can be classified by type systems, in the sense that there are type systems that only accept polynomial programs, for example. One more practical-minded offshoot of this research is RAML (Resource Aware ML), a functional programming language with a type system that will give you precise information of the running times of its programs. It is more precise, in fact, than big-O complexity, are constant factors are also included, parametrized by a cost model for the base operations.

You may think that this is cheating: surely some algorithms have a complexity that is very hard to compute precisely, so how could this language easily determine the complexity of its programs? The trick is that there are many ways to express a given algorithm, some which the type-system will reject (it rejects some fine programs), and some, maybe, that it accept. So the user doesn't get the world for free: he or she doesn't have to compute cost estimations anymore, but need to figure how to express code in a way that is accepted by the system.

(It is always the same trick, as with programming languages with only terminating computations, or provable security properties, etc.)