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I realize how hard it is to develop a CFG to model an arbitrary English sentence. Some valid discussion points for this topic can be found here:

Is there an EBNF that covers all of English?

However, I am interested in the most comprehensive CFG (if not complete) that covers the English language. Surely such a thing has been attempted by linguists, to various degrees of success. As an outsider to the field, I would imagine that there might even be an agreed upon "best approximation" CFG.

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    I don't think there's a comprehensive CFG. Most real world projects use statistical (or hybrid) parsers. There are, however, HPSG grammars with broad coverage. HPSG is an extension of CFG with grammars for quite a few languages. – Atamiri Jan 24 '15 at 21:24
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The treatment of English worked out in Generalized Phrase Structure Grammar by Gazdar, Klein, Pullum, & Sag is a CFG (with sets of rules given in highly abbreviated form) and is comprehensive in the sense that it includes the main areas of English covered in the TG literature. It is not a practical description, because there are too many rules, but it is a real unextended CFG. One of the main ideas was to show that transformations are not required to describe those constructions which they have in the past been used for. In my opinion, the book does that.

(Pullum, and perhaps the other three authors, came later to think that, after all, natural languages are not context free. I wasn't convinced though.)

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