(adding to the above)

Another downside of parser combinators, at least the ones that I wrote as a basis for Fortran parsing, is that if you implement them as C++ template classes, the types get astonishingly long in their names. This leads to long compilation times and makes debuggers very hard to use. Both of these concerns only affect the developer, of course, and seemed to me to be acceptable so long as the parser is fast and robust.

I'd use parser combinators again if I ever need to write a big parser, although I might not use overloaded operators (">>", "/") and confusing function names ("many" vs. "some") inherited from Haskell's Parsec library.