Doxygen. Because we started using it once in a while years ago without looking for alternatives, and it still works. Life is too short to spend time asking if a better tool exists for every possible thing.
The hard part isn't exporting documentation, it is writing useful how to use it. Any hints here would be useful. It is easy to parse C++ compared to the effort of writing useful prose about out APIs. (C++ is one of the hardest languages to parse, but compared to writing)