I'm one of those who reads the Appendices every time I read Lord of the Rings. Partly it's because of all the background info they contain on the fictional world: the fictional world, fully fleshed out, is what I read this for, as much as the story itself.
But partly I read the Appendices because they complete the story. They have extra little bits of key narrative tucked in here and there, such as the full tale of Aragorn and Arwen's love, and further info about what the Travellers did after coming back to the Shire. But more than that, the Appendices complete the novel, in a way, by allowing the reader to immerse himself or herself fully in Middle-Earth. "The Shire has been saved," Frodo says, "but not for me." But it is saved for the reader, and in the Appendices, we get it all.
One thing that hits you as you hit the hard road of the Appendices is the framing device. After a thousand pages of Tolkien's narrative you're lucky if you can remember that he ended the Prologue with that bewildering bit about the Red Book, and the Thain's Book, and the copy in Minas Tirith, and whatnot. Fictional historiography: dry stuff.
But then you read the Appendices, and they refer you back to the Prologue, and furthermore long sections of the Appendices' account of Numenor, Arnor, Gondor, etc., are given as direct quotations from something, and you realize, oh yeah, they're from the Red Book.
Then it hits you. The Lord of the Rings itself is meant - asks you to read it as - more or less Frodo's account, reworked in Rivendell and the Shire. I mean, sure, there's that scene at the end of the story proper where Frodo gives Sam the manuscript (Peter Jackson, admirably, retained it). But for me at least, it's not until I cross over into the Appendices and those significant quotation marks that I realize that everything that's gone before is meant to be read as a paraphrase of what's supposedly in this Red Book.
And that suddenly explains what is for me one of the most conspicuous features of The Two Towers and Return of the King. This is that Tolkien employs two very different prose styles for his narration. The chapters dealing with Frodo and Sam are written in the same style as Fellowship: detailed, novelistic narration, with lots of dialogue that sounds like authentic speech. Lots of description of place and feeling. The chapters in which Frodo and Sam don't appear - i.e., the sections in Rohan and Minas Tirith - are told in a more elevated, archaic, and in fact storybook style. Description of setting is often minimal, and conversations are rendered in a fair and graceful speech that you can't imagine anyone actually using.
I used to think this was a sign of two things that became true as the book wore on: one, maybe Tolkien was getting tired and rushed; two, as the deeds became greater, he decided to treat them in more of a legendary fashion. Because that's what it feels like: like you're listening to a storyteller. As opposed to the Frodo sections, which feel like you're reading a book.
But now - I don't know if this is what Tolkien intended, but I do think it fits - it seems to me that this stylistic divergence fits the frame device. The Rohan and Minas Tirith sections are things that Frodo didn't witness firsthand, things he learned about only later, through people telling him tales. It's only appropriate that the narration become more storybook-like here.
The proof, I think, is that the tone becomes most campfire-taleteller-like in scenes in which neither Merry nor Pippin are present. Exhibit A, I would say, is the first half of the chapter called "The Steward and the King." This is the part that tells of Faramir and Eowyn falling in love in the Houses of Healing. The tone here is perhaps the most elevated - courtly is the right word - of any section; you could almost be reading Malory. In terms of narrative, the tone actually weakens it, I think, because you can't really believe it as a love story in a novel, not the way you can believe, say, the courtship (deftly suggested through a minimum of details) of Sam and Rosie.
But if you think of it as a retelling of a retelling of a retelling of events that only the two principals really knew about (think of how your grandkids, or maybe your nieces, might one day tell the story of your own courtship), it becomes quite a charming passage, and a key part of the grand denouement of the novel.