Is there a Guinness (or otherwise) record for the longest discussion thread on an Internet forum?
Why don't you go to the Guiness site to find out and then let us know? We're busy here answering grammar questions.
LegacyDespite Blogger having said that the BHF threads would remain archived in read-only mode, the whole lot vanished on March 29, 2012
You might consider petitioning the NSA for the complete version.

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Sorry for the late answer, but it didn't exist when you posted the question.

The longest I have ever been aware of was a thread in The Coffee Shop category of the old Blogger Help Forum, titled "The Question None of Us Wants to Think About", with over 14,000 replies from March 27, 2010 until the last of the Google Help Forums platform was replaced with Google Product Forums on March 12, 2012.

I don't know for sure if it was the longest discussion thread on the internet, but it has been confirmed by a Google product manager that it was the longest (i.e. most replies) in the history of Google Help Forums. Despite Blogger having said that the BHF threads would remain archived in read-only mode, the whole lot vanished on March 29, 2012, and links to any threads now redirect to the landing page of the Blogger Product Forum on the Google Groups platform.

There are bits and pieces of it in various forum archive sites around the net; the most comprehensive seems to be at The Wayback Machine (archive.org).
 CalifJim's reply was promoted to an answer.
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Even as the previous reply was written, the discussion thread of comic #1190 at the XKCD forums was actually longer. By now, as I write this, they're at 2190 pages, of 40 posts each... do the math :-)

Actually, I'm pretty sure there are other threads that are far longer. The actual record is likely in the hundred thousands (if not the millions).
The Longest Thread Ever on stangetalk.net was started in Nov 2005, and is currently at 11,394 pages... 740,595 posts. It replaces another LTE thread about 1800 pages in length which was accidentally deleted by an admin.

The Thread was a sub-forum in MacWorld Forum called "Who Watches the Watchmen?"

started by MacJac when she insisted on inquiring the status us the upcoming movie that

ultimately spun-off into a free-wheeling Chat Forum called, "General Gabbery"

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