The author has a fascinating character in mind, and a story that is unquestionably that characterĺs, but for one reason or another, getting into their head just wouldnĺt pan out for the reader. Normally this is because:
The character is dead at the end of the story.
The author wants to keep the reader wondering what the character is thinking, or the character has a secret the author wants to keep from the audience.
Rachel from Baccano!. We mostly find out about the events aboard the Flying Pussyfoot from her report to the President of the Daily Days.
Subverted in The Rolling Bootlegs: while it appears that Maiza relating the story about his friend and subordinate Firo to a Japanese tourist, it's actually Firo himself telling the tale, and the tourist just assumed otherwise because Firo never properly introduced himself and was wearing glasses like Maiza's.
Rock in Black Lagoon. The story is told from his point of view but it's pretty obvious the protagonist is Revy. As if the opening and ending animations being all about her wasn't enough to tip you off. The "Why is he watching her so closely?" angle is played deliberately.
Later chapters though are more focused on Rock and he becomes quite an interesting character himself, making him more of a Supporting Protagonist.
Souryo Fuyumi's manga Cesare is about a sixteen-year-old Cesare Borgia, his servant Miguel, and the games of Xanatos Speed Chess the two are playing with various historical figures. It's actually told by Angelo, some kid who's at school with them (readers usually hate Angelo, which may or may not be intentional). This is one of those uses where it starts to seem like the Ishmael is a little too fascinated, though this too may be deliberate.
Saji Crossroad becomes this during the second season of Gundam 00. The main character is obviously Setsuna F. Seiei. Saji also pilots the support machine for Setsuna's eponymous mobile suit which acts as its catalyst.
Sakuno Ryuzaki, and the Freshmen Trio from Prince of Tennis (at least initially). Ryoma Echizen's undeniably the focus of the story, but his personality and development are mostly viewed through other characters due to his aloof nature.
Eva Procorpio has become this in Shakara - while Shakara is undoubtedly the protagonist, the story was primarily told through Eva's narration shortly after she was introduced. Then she started getting more screentime than Shakara.
Evey Hammond in V for Vendetta - V is certainly the lead character, but the story follows Evey as exposure to V changes her.
Sexton Furnival in Death: The High Cost of Living. Death/Didi is the axis around which the story revolves, with Sexton just having been dragged in after her. But he's the one with real Character Development; hanging out with Death for the day renews his interest in living, rather than committing suicide out of sheer ennui like he wanted to do at the beginning.
Stalag 17. The real protagonist of the movie is the Anti-Hero Sefton. The story is narrated and seen through the eyes of his "sidekick" Cookie, a character so bland that his name appears dead last in the IMDb cast list for this movie.
David Cronenberg is fond of this trope, often telling his stories from the perspective of the romantic interest of the real lead.
Frank Carveth in The Brood. The actor, Art Hindle, isn't even mentioned on the cover, while Samantha Eggar and Oliver Reed (who were both bigger-name actors and play more interesting characters) get top billing.
A subversion in Fight Club: the film seems to be about Tyler Durden, and The Narrator just tells his story. But it turns out they're the same person.
In Tangled, Flynn claims, in the opening narration, that it's not really his story, it's Rapunzel's.
It Could Happen To You is narrated by Angel Dupree, a reporter and photographer working undercover as a homeless man and writing about the main characters. It's actually something of a twist that there is a first person narrator rather than a third person omniscient one - Angel Dupree doesn't get introduced as a character until near the end of the film, and he never refers to himself in his narration prior to The Reveal.
Robert the Bruce in Braveheart, a minor secondary character throughout the movie, reveals himself at the narrator as the end and informs us that he ultimately carries on William Wallace's mission by defeating the English.
42: Wendell Smith, an African-American sportswriter hired to accompany Jackie Robinson, is a recurring character in the movie and provides bookends for the beginning and end.
Verbal Kint in The Usual Suspects has exactly this relationship to Kaiser Sozye...but there's more to it.
The viewpoint character in the archaeology segment of the Interactive Fiction work The Beetmonger's Journal is a textbook First Person Peripheral Narrator; they're largely a complete cipher, and present primarily to chronicle the exploits of the more dynamic Lapot, and the other viewpoint character — the eponymous beetmonger — as dictated to them by Lapot from a journal they discovered.
Ishmael in Moby-Dick. He stops participating in any of the events in the story entirely half way through the book, describing scenes that he couldn't possibly have been present to witness, and only becomes involved with things again in the book's epilogue.
Dr. Watson is First Person Peripheral Narrator to Sherlock Holmes, in addition to being - appropriately enough - The Watson. Most of them, at any rate. The few with Holmes himself as narrator show the "appear conceited" problem in great splendor.
Dostoyevsky's The Posessed (a.k.a Devils) has an unnamed narrator who has a minor role in the events, but he knows everyone and described a lot of scenes he hasn't witnessed... ahem.
Dostoevsky likes this technique. The Brothers Karamazov uses the same shtick, with an unnamed narrator implied to just be someone who has lived in the town for many many years and knows all the local gossip, but for all intents and purposes is effectively omniscient.
The so-called "protagonist" of the book version of The Island of Doctor Moreau does nothing but get thrown overboard, land on an island and watch more interesting people do experiments; Moreau and his experiments are the actual protagonists.
The various film versions tend to give him a more active role, sometimes as Moreau's final experiment (and success)
Weirdly, Lockwood and Nelly in Wuthering Heights. The main story (about Cathy, Heathcliff, Edgar and that lot) is being told to Lockwood - an outsider to the area - by Nelly, a servant whose active role in the story varies a lot.
Even more weirdly in the same novel, by Isabella, who writes a note about her time with Heathcliff later found by Nelly and recited from memory to Lockwood. Also, the contents of the entire novel are really Lockwood's diary. That's right — the reader reads a diary of a man who faithfully records lengthy monologues by a character who in turn faithfully relates a pages-long letter she herself read years ago. Lampshade Hanging?
There are two main viewpoint characters in Men at Arms; neither of them is the real protagonist of the story, Carrot.
Originally Carrot was going to be the viewpoint character, but then Pratchett decided it would be more interesting to leave his thoughts out of the narrative, and shifted the viewpoint to Vimes. This ended up having very interesting results. In fact, in the entire series, there is exactly one page written from Carrot's point of view, even if the story is revolving around him. Sometimes the book spends some time on other characters' thoughts on what Carrot is thinking, because he's like a well: both extremely simple, and extremely deep.
Some of John Wyndham's works use this, most notably The Midwich Cuckoos, which is told by a fairly uninspiring and relatively uninvolved observer. If the book can be said to have a protagonist, it would have to be Zellaby.
Jenny in Nothing's Fair in Fifth Grade. While we get to relate to some of her own life problems and situations, the story is really mostly about Elsie, the overweight girl with significant life problems, whose life gradually improves (via Jenny). Jenny's Character Development is largely based around her relationship with Elsie.
Subverted in the first ArsŔne Lupin story. It begins as a very traditional example of a mystery story using this trope, where a nondescript male narrator is describing Lupin he is actually Lupin himself, and has been spreading to the police inaccurate descriptions of his appearance.
The nameless sailor listening to Marlowe tell the story of Kurtz in Conrad's Heart of Darkness. Marlowe himself is also an example, as his main role is just to witness Kurtz.
Marlowe does this again in Lord Jim.
This also applies to Marlowe's equivalent character, Willard, in Apocalypse Now.
Fried Green Tomatoes at the Whistle Stop Cafe and its film version (simply called Fried Green Tomatoes) has two perspectives; a woman at a nursing home, and the old lady who tells the woman her story. The old lady's stories are mostly about her adoptive sister and her relationship with another girl.
The H. G. Wells novel The Time Machine is set up as a frame tale narrated by another, who relates what the time traveler has told him about his adventures.
Similarly, his short story The Door In The Wall is told by someone whose friend is seeking the eponymous door.
The Mad Scientist's Club by Bertrand R. Brinley; Charlie serves as the narrator, while Henry Mulligan serves as the protagonist.
Captain Alatriste's squire ═˝igo de Balboa, although ═˝igo sometimes furthers some plots himself.
Richard MacDuff in Dirk Gently's Holistic Detective Agency, whose main purpose is to be completely bewildered by title-character Dirk. In the second book, this device is abandoned, and it turns out Dirk himself is a lot more bewildered than he lets on.
Susie, the narrator of The Lovely Bones, is dead and in heaven. Most of the book is her following her friends and family as they deal with her death and move on, as well as the man who raped and killed her.
Robert A. Heinlein may have been trying to do this in his novel Podkayne Of Mars, with the title character being First Person Peripheral Narrator for her Evil Genius younger brother Clark. It didn't really work, because she ended up being too strong a character to be overshadowed.
Leo Borlock, the narrator of Stargirl by Jerry Spinelli, is a First Person Peripheral Narrator for the title character.
All four narrators of The Sound and the Fury are intended to be this, as William Faulkner always said the book was really about Caddy. However, it's an unusual example of this trope because Caddy's barely there to be seen even through the eyes of the other characters — it's mostly about the impact her actions have had on the family.
Because what I am trying to tell you... What I have been trying to tell you all along is simply that my father, without the slightest doubt, was the most marvelous and exciting father any boy ever had.
Nanapush and Pauline takes turns narrating Louise Erdrich's Tracks, but the story revolves around Fleur Pillager.
Richard Papen from Donna Tartt's The Secret History. The story is unquestionably about the other students in Professor Julian Morrow's clique, all of whom are far more sinister and have way more secrets, but Richard is our narrator.
Fanny, the narrator of Nancy Mitford's Love In A Cold Climate and The Pursuit of Love, tells the stories of Linda, Polly and Cedric and only mentions concurrent events in her own life - such as her marriage and the birth of her children - in passing.
The Everworld series has four. The primary four protagonists,(David, Christopher, April, and Jalil) are only protagonists at all, or indeed, in Everworld in the first place, because of they are all associated (in different ways) with the witch who binds all of the story and character arcs together, as well as the rest of the two universes. Averted later in the series when the witch in question finally narrates a book, and Subverted in the eleventh when the author Drops A Bridge On Her and focuses on the four First Person Peripheral Narrator in the twelfth book entirely, instead.
Phineas is the First Person Peripheral Narrator in John Halifax, Gentleman, a Victorian novel by Dinah Craik.
In The Master Of Ballantrae, the story is told after all the important characters are dead by Mr. McKellar, the steward of the Durrisdeer estate, because he wants to set the record straight and clear the reputation of the late Lord Durrisdeer. McKelllar narrates the events he was present at in the first person, and his actions have some influence on the course of events, but he's not central.
Tim Wynne Jones's short story "Save the Moon for Kerdy Dickus" begins with the line "This is Ky's story." — Ky being a friend of the young narrator, and her story being about a Stranger who came to Ky's family's house one evening and thought that they were aliens. The friend telling the story was not there for the main events of the story at all. The First Person Peripheral Narrator perspective is effective here because, as the narrator says flat out in the first paragraph, "In this story, the way things look is really important," and the fact that the narrator is neither as familiar with those things as Ky nor as unfamiliar with them as the Stranger emphasizes the fact that this story is all about the perspective from which it's told.
Just about all of H.G. Wells' books, including the above-mentioned Island of Dr. Moreau and The Time Machine, use this trope. Perhaps the only novel to avert this is The War of the Worlds, where the unnamed narrator is the protagonist by default because no other major characters last for more than a handful of chapters or have any real motives or character development.
To Kill a Mockingbird has Scout watching her father's heroic attempt to save Tom Robinson's life. Scout does have her own adventures, but Atticus is the real man of action.
Elmore Leonard's "Hombre": mainly for reason #2, as a big part of the point is John Russell's unwillingness to let anyone else see what he's thinking, or who he really is.
The Hyperion Cantos novel Endymion has Raul as the First Person Peripheral Narrator to Aenea.
One of the popular criticisms of The Tenant of Wildfell Hall is that the frame narrator Gilbert Markham should be this trope, but instead, he eventually becomes the protagonist Helen's love interest. Note Gilbert was created by the sister of Lockwood's creator.
In Robert E. Howard's Conan the Barbarian story "Beyond the Black River," Balthus — until he gets killed near the end. Many of the stories introduce Conan with such a character, who often lasts a long time into the story before we get Conan's POV.
In Gene Wolfe's Book of the Long Sun, Silk is the protagonist but two of his pupils, Horn and Nettle, turn out to be the narrators.
Although Michael is the title character, Beau Geste is told from the perspective of his younger brother because that's the only one of the three brothers to survive the entire story.
Barbara Robinson's three Best novels (most famously The Best Christmas Pageant Ever) are all about the Herdmans, a group of misbehaved siblings with a difficult home life, as they interact with their town's other children. The books are narrated by a girl in their class, however, who relates information about the family and the children's various antics as the plot of each book unfolds.
Gil Abad in the Spanish novel series Marijuli & Gil Abad. Despite being one of the eponymous characters, he's a Watson at best. The (few) chapters that aren't written under his point of view are all in a different font, to make this tope even more obvious.
Jim Burden, in My ┴ntonia, has touches of this. His narration speaks mostly of the fascinating people around him than of his own life, though it is clear from some throwaway lines near the end of the book that he has had an interesting one.
Dunstan, the narrator of Fifth Business, could be considered this. He himself doesn't really do much, but the accompanying stories of Percy and Paul detail a story of revenge that takes sixty years to conclude. The title even references this; "fifth business" is a stage term meaning that one character who has no real part to play in the story except for the fact that they know a game breaking fact about the main character.
Haldeth of The Master of Whitestorm played this role when in Korendir's company. When apart, Korendir's story was always told in third-person.
The narrator in Aphra Behn's Oroonoko doesn't even get a name, even though we're clearly supposed to identify her with Behn herself. Either way Behn spends pretty much the entire novella gushing over the enslaved title character's nobility and strength (to the point where the subtext rapidly starts becoming . . . text) and describing events she couldn't possibly have seen (specifically events occurring in West Africa before Oroonoko and his beloved Imoinda were enslaved, and therefore the narrator would have been halfway around the planet from).
Umeed in The Ground Beneath Her Feet skates this as he tries to tell the story of his life in the shadow of his friends Vina and Ormus, the world's greatest rock stars.
Oelph is this in the Culture novel Inversions, to the more mysterious character Doctor Vosill. In the other narrative however DeWar is his own viewpoint character (ostensibly the story is being related by someone else, but it has no effect on the presentation).
From the Mixed-Up Files of Mrs. Basil E. Frankweiler by E.L. Koingsberg revolves around two run-aways who hide out at the Metropolitan Art Museum in New York City, but is narrated by the eponymous character, who doesn't show up until the last few chapters of the book.
The actress Deirdre is the most important character of No Woman Born, but her perspective is not given because she was recently resurrected in a cybernetic body. Because the central conflict of the story is whether Cybernetics Eat Your Soul, we instead watch from the eyes of her manager John Harris, so we too can be in the dark about whether she's truly there.
A few of Black Company novels come across this way. Raven is at least as important as Croaker in The Black Company and Shadows Linger and definitely outshines Case in The Silver Spike. This was mostly likely done because Raven fakes his death in the first two books and because Case's Distant Finale is more relevant to the series in the last.
The Warhammer world's Gotrek & Felix series (created by William King, resumed by Nathan Long for several books, now written by many authors) uses this trope as its foundation. The Dwarf Gotrek Gurnisson is, without doubt, the central protagonist. Gotrek is a slayer - a dwarf who has committed some great shameful act and seeks to atone for this dishonour by dying in battle against worthy foes. The stories are all driven by his obsessive quest to confront the most powerful monsters and villains he can find - encounters which he invariably survives, thanks to being a hugely muscled slab of frustrated dwarfish violence with one of the most powerful magic axes in the world. The stories are not told from Gotrek's perspective, however, but from that of his companion Felix. Felix Jaeger is a veteran adventurer, but still a fairly normal human - a one-time poet and minor political agitator who became caught up in Gotrek's quest when Gotrek saved his life and he swore a drunken oath to record the slayer's doom in an epic poem. As such a lot of Felix's thoughts on their adventures are of the "I can't believe I'm still here" variety, often shading into "yes, but if Gotrek does succeed, then I'm almost certain to die at the hands of whatever killed him". Using Felix as the point-of-view character makes Gotrek far more mysterious, unfathomable and unpredictable, as well as keeping his dark secret - the shame that made him become a slayer in the first place - still secret. Even after decades of adventuring together, Felix still doesn't know what Gotrek's shame really was.
Live Action TV
The new series of Doctor Who starts with the episode "Rose", which has the title character as The Watson and First Person Peripheral Narrator to ease the audience into the series.
In fact, the first few episodes featuring any new companion do a bit of this, as the Doctor has to re-explain who he is and what he does. A change in companions is a much better time for new viewers to get into the show than a change in Doctors.
Unless, of course, both changes happen at once, like with the Eleventh Doctor.
The Doctor Who Expanded Universe novels are typically all written from the perspective of the companions, or the random characters trying to work out what these weirdos are about. Lampshaded in one novel set in the Land of Fiction, where the Master of the Land of Fiction laments (in the descriptive text) that even in Omniscient Narrator mode, he still doesn't know what the Doctor is thinking.
The WB/CW teen drama Everwood was narrated by a peripheral character who was involved with the main characters, but was old and wise enough to give the series a grander perspective than any of the core characters could have. There were occasional voice-overs from other characters in the form of letters between characters at times.
The BBC radio drama adaptation of His Dark Materials has the character Balthamos (in this version described as a "recording angel" who observes and describes events as they take place) as the narrator, usually just observing and describing events that takes place, unseen and unheard by all, until he chooses to reveal himself to them and involve himself directly in the events as a character. Whenever he does this, there seems to be a slight gap between Balthamos as a narrator and Balthamos as a character, as if he's somewhat dispassionately continuing the observation and narration in his head — even describing events that take place elsewhere and he's clearly not physically present for — even as he is interacting with the other characters and reacting with much greater emotion outward.
In the musical Rent, Mark is an aspiring filmmaker who passively observes the dramas and adventures of the rest of the cast while he films them. His role is to narrate to the audience and reflect on their situations.
Most of the actual story in Diablo II is narrated by Marius, a random person whom the Dark Wanderer (Diablo) takes along to carry his stuff or something. He is eventually given the task to enter Hell itself to destroy Baal's soulstone, ie. to actually do something, but understandably chickens out. What's interesting is that if Marius is seen as First Person Peripheral Narrator, then the main character is Diablo, not the Player Character. But since the latter only runs around killing monsters and misses all the real story, even Marius himself seems more like the protagonist at times.
The ending to Valkyria Chronicles reveals that the whole thing has essentially been the scrapbook of Ellet, a (somewhat annoying) journalist who had made it her mission to document Squad 7's adventures.
The narrator of Narcissu, who is not even given a name in-game, largely serves as a chauffeur and plot-catalyst for the real focus of the story, Setsumi. Justified by reason #1 above. Setsumi herself fits this role to some degree vis-a-vis Himeko in the prequel, but she does at least get quite a bit of character development. This is a bit less so in other adaptations.
Innocence Smith in Mars: War Logs. He's the sidekick to player character Roy Temperance for much of the game. After the opening cutscene he doesn't narrate much, but he does recount his and Roy's escapades in his diary. If you screw up and Innocence is sent into exile, though, Roy recovers the war log, starts writing in it, and narrates the final cutscene.
Cecil, host and narrator of Welcome to Night Vale, reports all the news, gossip, and horrifying calamities going on in town, but rarely does much himself since he's usually in his radio booth when the most... exciting things are happening. This is sometimes a real source of frustration, such as when his beloved Carlos is in danger.
Pvt. Robert "Paperboy" Higgins from Roughnecks: Starship Troopers Chronicles is a FedNet reporter, basically embedded with the Mobile Infantry (except he's an enlisted man, not a non-combatant). Most of the show's narration is him speaking in the past tense, as though writing his memoirs, and he states in the first episode, regarding his comrade and the obvious male lead Johnny Rico, "I know he doesn't look like much now, but trust me, this guy's gonna be a legend."
The Narrator (a pudgy snowman) in the famous Rankin/Bass animated adaptation of Rudolph the Red-Nosed Reindeer. Apparently, his only raison d'etre besides telling the audience the story is to sing and perform on the guitar songs that are only tangentially related to the plot. The story's real protagonist, of course, is Rudolph.
Several episodes of Batman: The Animated Series do this such as "The Man Who Killed Batman" or "It's Never Too Late," taking place mainly from the viewpoint of a minor or one-shot character.
The Tom and Jerry cartoon "Blue Cat Blues," about Tom committing suicide after a failed romance, is told from Jerry's narrative.