The Hitchhiker's Guide to the Galaxy: All versions begin with the Vogons announcing the impending demolition of Earth to make way for a hyperspace bypass through the Solar System, just so they can put a tick in a box next to this item. In the book series only, the plan was unsuccessful as Earth was on a faulty probability axis, and so the series ends with the Vogons demolishing Earth in EVERY probability and finally putting the tick in the box.
Finnegan's Wake ends with a half-finished sentence that is completed by the book's first sentence, so it's more of a loop.
Lolita begins (in both the foreword and the novel proper) and later ends on the eponym; the foreword begins, "Lolita, or the Confession of a White Widowed Male, such were the two titles under which the writer of the present note received ..."; the novel proper begins, "Lolita, light of my life, fire of my loins. My sin, my soul." and ends "And this is the only immortality you and I may share, my Lolita."
The first and last sentences of Isabel Allende's novel The House of the Spirits are exactly the same: "Barrabás came to us by sea...."
The Warhammer 40,000 novel Desert Raiders uses the first paragraph of the book in its epilogue to show that a Tallarn regiment had traveled back in time through the Warp to create the very incident they were supposed to be investigating.
Near the climax of Inheritance, Eragon impales Galbatorix on his sword, much like he did Durza at the end of the first book. The phrasing itself is nearly identical.
Eragon's dream the night his uncle dies is the final scene in the last book.
Harry Potter: Voldemort dies as a spell intended to kill Harry Potter backfires. Now are we talking about Philosophers Stone or Deathly Hallows?
Then, after a years-long timeskip, young Potter leaves to attend the same school as his parents.
Harry Potter and the Philosopher's Stone, Ron to Hermione, "ARE YOU A WITCH, OR NOT?!", during the buildup to the climax. Harry Potter And The Deathly Hallows, Hermione to Ron, "ARE YOU A WIZARD, OR WHAT?!", during the buildup to the climax.
At the start of the first book, Hagrid carries baby Harry to his relatives' home. Near the end of the last book, Voldemort forces Hagrid to carry the seemingly-dead Harry back to Hogwarts.
Prisoner of Azkaban begins with a lot of owls giving post to Harry. It ends with more owl post for Harry (and a bit for Ron). The chapters are even called "Owl Post" and "Owl Post Again."
Ginny Weasley's first appearance in Harry Potter and the Philosopher's Stone has her at Platform 9 3/4 begging her mother to allow her to go to Hogwarts. Her last appearance has has her at Platform 9 3/4 with her own daughter begging her to allow her to go to Hogwarts
Also literally: if you look at the American first-edition book covers for Sorcerer's Stone and Deathly Hallows, they've both got curtains surrounding the images, for beginning act and ending act.
Watership Down opens with "The primroses were over," and ends with "where the first primroses were beginning to bloom."
The first book in The Dark Tower opens with "The man in black fled across the desert, and the gunslinger followed." The last book ends with those same words because the entire series is a "Groundhog Day" Loop (with a small twist).
Phedre is sold into slavery to a barbarian ruler with plans of conquest and makes an unplanned attempt to kill him in his sleep, which fails, in Kushiel's Legacy; in Kushiel's Avatar, she intentionally gets herself enslaved by a barbarian ruler with plans of conquest, murders him after gaining his trust, and frees the remainder of his prisoners.
A more subtle example: Each book in the Mage Wars trilogy by Mercedes Lackey and Larry Dixon begins and ends with the same word: "silence" in the first book, "light" in the second, and "freedom" in the third.
These might be considered, roughly, Arc Words for each book, at least for the first and last — the first is the story of the "Mage of Silence" who created gryphons, and the third is about the children of two famous characters trying to break free from their parents' expectations and reputations.
In Monica Hughes's Invitation to the Game ends with the main character writing the first letter of the story itself.
The third book of Traci Harding's trilogy ''The Ancient Future", ends with Noah/Selwyn reading out the first line of the first book.
At the beginning of Number the Stars by Lois Lowry, Annemarie is running playfully with her friend on the street. At the end, she's running to deliver a package that will allow the friend's family to escape the Nazis.
The book The Heart of Valor by Tanya Huff has scenes at the beginning and ending that are introduced almost exactly the same way: the main character, a Marine, is on a balcony in a space station looking down at the new recruits.
A Memory of Light closes with an inversion of the opening narration of each book in the series.
It was not the ending. There are neither beginnings nor endings to the turning of the Wheel of Time. But it was an ending.
Blade of Tyshalle by Matthew Woodring Stover has the "A tale is told of twin boys born to different mothers" passage appear right after the book begins (after the ending quotes) and right before it ends (second-to-last page).
The Hobbit begins and ends with Gandalf visiting Bilbo in his home at Bag End.
Also, both The Hobbit and The Lord of the Rings start with a party (with correspondingly-similar chapter titles), and if you have one of the printings where the first chapter of LOTR is stuck onto the end of The Hobbit, that's at least one more right there.
The Demonata book Bec begins and ends with the book's tagline "Screams in the dark". The first time is the titular charecter/narrator (who possesses perfect recall) recounting the tale of her birth. The last time is when she is being slowly eaten alive by numerous demons while trapped in a collapsed tunnel.
A Darkling Plain ends with Shrike recounting the opening sentence of the first book in the series word-for-word.
Starship Troopers, the book, begins with Rico as a soldier being briefed by his lieutenant and preparing for a drop, and ends with Rico as a lieutanant briefing his soldiers for another drop.
The Outsiders end reveals that the book is an nonfiction essay the protagoinst wrote for school; it ends with the same sentence as the beginning as he reports that he wrote down "[the first sentence...]".
"When I stepped out into the bright sunlight from the darkness of the movie house, I had only two things on my mind: Paul Newman and a ride home..."
The Pillars of the Earth: The book begins with a hanging, and the second-last scene in the book is another hanging. The first sentence in both scenes is the exact same.
The second Sherlock Holmes novel, The Sign of Four, begins and ends with Holmes bored and taking cocaine. This is used to emphasize the fact that although, as Watson says, Holmes is the one who "did all the work in this business," he's also the only one who doesn't seem to get anything out of it.
Baltimore, a novel by Mike Mignola and Christopher Golden uses a tense for this: the beginning and ending sections are both written in present tense, versus the rest being written in past tense.
The British publication of A Clockwork Orange begins and ends with almost exactly the same passages, only with different names for the people in his gang. Several chapters, including the first and last, also start with the phrase, "So, what's it going to be then, eh?"
Just a note, not every publication of this book includes Chapter 21 (at least, not in America). In other words, it doesn't end with a similar passage to the beginning. However, most, if not all, recent publications generally include it.
The Shadow of the Wind begins and ends with almost identical scenes where a man takes his young son to the Cemetery of Forgotten Books.
Alien Bodies begins with the Third Doctor on a distant, peaceful, deserted planet, burying Laika, the Russian dog who became the first living creature to leave Earth's atmosphere and who died in the attempt. The book ends with the Eighth Doctor carrying out a wake on the same planet for himself.
The Deltora Quest series ended, with a "Where Are They Now?" Epilogue, in which the description of Leif's reign uses most of the same wording as the description of King Adin's reign in the first chapter of the first book. The final chapter in the series is even called "Full Circle".
Nick Kyme's Warhammer 40,000 novel Salamander opens and ends with the death of their captain from treacherous attacks, and the company's coping with it. Coping better at the end than the beginning.
In Stephen King's The Green Mile, Paul Edgecombe originally bookends the manuscript he's writing, starting and ending with, "This happened in 1932, when the state penitentiary was still at Cold Mountain. And the electric chair, of course." However, the events of the book conspire to have him write of the mouse and his blessing from John Coffey.
King does this again in Needful Things, with a narrator telling the reader about the people in town and a new shop that's about to open. At the start of the book, it's Castle Rock, Maine. At the end, it's Junction City, Iowa (the setting for the story "The Library Policeman", in Four Past Midnight).
Beyond the Western Sea begins "Just before dawn - that moment when time itself seems to stand still, when the whole world teeters on the edge of possibilites. . ." and ends with "She felt herself teetering on the edge of possibilites."
In Neil Gaiman's Neverwhere, the book begins and ends with Richard going out to a bar with friends, disliking it, going outside, a friend coming out to see him, and something uncanny happening, though the sequence of the last two are reversed.
In Isaac Asimov's short story "In a Good Cause—", there is a short prologue-scene (in italics), of which the first sentence is led into at the end of the main story and repeated verbatim (also in italics).
The Da Vinci Code begins and ends with a dead body in the Louvre. The first time it's Jacques Sauničre's. The second time it's the corpse of Mary Magdalene, whose tomb was hidden under the Louvre by the Priory of Sion.
Titus Groan begins and ends with Mr. Rottcodd's solitude being disturbed, first by Flay's arrival with news of Titus's birth, and again by viewing the aftermath of Titus's Awesome Moment of Crowning through the window.
One Day starts and ends with Emma and Dex's first day together in 1988.
The Elenium begins and, except for the epilogue, ends with Sparhawk slinking into Cimmura on a rainy night. The Tamuli begins the same way.
A perfect example would be The Name of the Wind, as the epilogue, and the prologue, named The Silence of Three Parts have the very same descriptions in each of them, only slightly changed to suggest the tone of the book.
The Dresden Files: A subtle one, but Turn Coat begins with Harry saying, "I know what it feels like to have the Wardens on your ass for something you haven't done." The book ends with Morgan's dying words being, "I knew that you knew how it felt to be an innocent man hounded by the Wardens."
The last section of The Redemption of Althalus has Althalus going back in time to replay the adventure that ended with his meeting Ghend in the first section of the book, and making it end differently this time.
The Barsoom Project opens with a battle scene from the first Fimbulwinter Game, in which a club-wielding Adventurer is killed out by the Terichik. At the end of the book, the second Fimbulwinter Game kicks off its own climactic battle with an identical scene using the same lines of narration, except that this time it's Max who dies.
The His Dark Materials cycle begins and ends with the name of the protagonist: Lyra and her daemon moved through the darkening hall. [...] "The Republic of Heaven," said Lyra.
Aunt Dimity and the Deep Blue Sea opens with Lori fielding balls while her sons play cricket (since she can do little else in the game). At the end of the book, Lori speaks of rejoining her sons in their backyard play, but says she can bowl a wicket clean nine times out of ten.
Aunt Dimity Slays the Dragon opens on a boring committee meeting, where the villagers are planning for another summer of events, which promise to be just like last year's (and the year before that...). The book closes with Lori and her neighbours actually looking forward to the next committee meeting, since their fun-yet-hectic renaissance summer is over and Guy Fawkes Day is fast approaching.
A Game of Thrones, first book of the Song of Ice and Fire series, in the beginning, Eddard Stark punishes a deserter by decapitating him. Near the end of the book, Eddard is decapitated.
In Of Mice and Men the book begins in the clearing by the Salinas River. However, at the start, the sun is rising and at the end it is setting.
The first book of Jennifer Roberson's Tiger and Del series begins with Del walking into a cantina looking to hire Tiger. One of the last scenes in the fourth book (which was the final one until some years later) begins with Del walking into a cantina looking for Tiger, including the same poetic description of Del, but this time she's here to tell him she's booked a ship and they can go off to their new life together.
The first and last chapters of The Spook's Battle begin with Tom being chased through a wood, but in the former, it's Tom's friend Alice, and it's a training exercise, while in the latter, it's Grimalkin, and for real.
The first book, which introduced us to the Warriors world and the main character Firestar, was written by Kate Cary (out of the several authors that make up Erin Hunter). The last book in the main series, The Last Hope, which ends with Firestar's death, was, fittingly, given to Kate to write.
The Power of Three story arc (which covers the two series Power of Three and Omen of the Stars) begins with the characters learning the prophecy "There will be three, kin of your kin, who hold the power of the stars in their paws." The final lines of the last book echo this, and the series in general:
There will be three cats, kin of your kin, with the power of the stars in their paws. They will find a fourth, and the battle between light and dark will be won. A new leader will rise from the shadows of his death, and the Clans will survive beyond the memories of his memories. That is how it has always been, and how it always will be.
In the Discworld book Sourcery, the book starts with the sentence "There was a man and he had eight sons" close to the end of the book, someone is telling a story that starts with the same sentence.
Robert A. Heinlein's Starman Jones begins with Max Jones lazing, one sunny evening after finishing his chores, on a slope overlooking the spaced rings of a magnetically levitated supersonic "ring train" waiting for the Tomahawk to shoot through. It ends with assistant astrogator Jones on the same slope waiting for the Tomahawk once more. It's set up so the first paragraph of the last chapter reads as though it was All Just a Dream but then provides a "Where Are They Now?" Epilogue for the story.
Glen Cook's The Black Company is a series of ten novels with a total of five narrators between them. That said, a single narrator tells the stories of the first four books...then comes back for the tenth and final novel, the responsibilities that kept him from narrating the others finally discharged.