Compiled Documentation
Compiling usable products from source files is a necessary reality in the context of software. Computers cannot run code without processing it into machine instructions.
Documentation has no such technical requirement, and these days, even software is sometimes "compiled" at run-time. Nevertheless, there is, I think, benefit in building publication systems that require compilation, as compilation allows us to automate some tasks in a clear way and requires a certain kind of approach to building documentation. These are both good things.
Advantages of Compiled Documentation
Editors, writers, and subject matter experts can review documentation as a gestalt, prior to publication. If such resources are atomic, this is incredibly important: in a more dynamic model, it's difficult to update a number of documents at a time. Compilation solves this.
Compiled documentation resources are faster because the system does not need to render the content on every view, and its easier to present static documents in offline formats (e.g. PDF and eBook formats.)
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Disadvantages of Compiled Documentation
The compilation process, particularly for larger projects where documents are heavily processed, can take a long time.
It is sometimes difficult to work with short-feedback cycles during the writing process. Though local compilation, and other facilities can help, if you want to be able to see how a document will render continuously, that's difficult. (on the other hand, if your build system is so unpredictable that you can't quickly learn how it will build documents, that might point to a different problem.)
Compilation centralizes the documentation work flow. In a wiki everyone can press the "save" button, in most cases; in compiled systems there is probably only a small handful of people who can publish documentation.
While this may be a disadvantage, in practice only a small handful of people actually edit most wikis, and with properly automated build and deployment processes it's possible to make compiled documentation easier to use.
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Resources and Examples
ikiwiki (wikis aren't necessarily good for documentation, but ikiwiki is a great piece of software that handles publication in a useful way.)
jekyll, hyde, mango, and nanoc (blog site-generators/publishing-systems aren't necessarily good for documentation, but are interesting examples of compiled sites.)