Possibly the Ur Example is William Shakespeare's Falstaff, the fan favorite Butt Monkey of his two Henry IV plays. Falstaff unceremoniously dies offstage in Henry V without uttering a single line. Readers and critics speculate that Shakespeare was probably worried about Falstaff upstaging his main character (as he arguably does in the other plays).
Happens to the hero of Edmund Rostand's Cyrano de Bergerac, although there it was a log, not a bridge. Cyrano lampshades the dissatisfying irony to the end of such a life as a fearless swashbuckler. Rostand's hands may have been tied by the fact that the actual Cyrano de Bergerac was killed in that very manner.
Alastair Reynolds's Revelation Space series is frequently accused of this. In one case, a minor arc of one novel involved one of the protagonists falling in love with another character, who was subsequently killed off between novels in an apparently random accident.
Something similar happened between So Long, and Thanks for All the Fish and Mostly Harmless. Arthur Dent's love interest Fenchurch is taken from him because of some technicality that doesn't really make a whole lot of sense even in context. Douglas Adams later apologized for this and blamed it on the fact that he'd been having "a thoroughly miserable year" when he wrote the latter book.
There's also the fact that Mostly Harmless ends with all versions of the Earth in all parallel universes being destroyed along with most of the main characters (except Zaphod, because he wasn't there) before they managed to accomplish any of their goals in that book. I mean, sure, there's now a sequel by a different author. But, still...
Donald Gennaro, of Jurassic Park. In the book he's not a cowardly jerk as in the movie; he helps Muldoon against the Tyrannosaur and the raptors, and escapes the island with his life. In the second book... he got dysentery and died. A similar fate befalls Muldoon. Noteably, both characters survived in the book but were killed by the dinos in the film, which makes it look like Crichton was cleaning house to make the two sync up better.
Tom Navidson's death in House of Leaves is very mean-spirited. Three words: OM NOM NOM.
Johnny Truant, however, is an Unreliable Narrator transcribing the work of an Unreliable Narrator — and one of them, probably Truant, considered making that particular scene even worse: by spearing the children on one of the house's non-euclidean corners beforehand. The choice not to do this, it must be pointed out, seems to have been utterly arbitrary.
At the end of Anthony Trollope's The Warden from The Chronicles of Barsetshire, major character John Bold has just married into an influential Barsetshire family and can be expected to play a major role in future novels. By the beginning of the next book, Barchester Towers, he's dead of causes never mentioned in the book, leaving behind a plot-convenient widow and young child.
In the Eisenhorn trilogy, Midas Bentancor gets killed between Xenos and Malleus, with details being vague. However, this gets used effectively, as it provides a lot of development and motivation for his daugther, Medea.
The death of Locklear in The Riftwar Cycle was done to get him out of the way so William could become Knight-Marshal of Krondor for the Serpentwar.
And then in the Serpentwar Saga Greylock was SHOT THROUGH THE HEART by a crossbow bolt fired by one of his own troops, after the day is won, because the trooper just shouldered his crossbow rather than unload it. Somehow a bolt fired blind, backwards, from an * upside down* crossbow, by a foot soldier, went straight through the chest of his (mounted) commanding officer.
To say nothing of the Empire Trilogy. Ayaki, right at the beginning of the third book, anyone?
Not to mention Miranda in Rides a Dread Legion, whose throat was ripped out by a random demon that jumped on her back after the big bad was dealt with.
In The Dresden Files, Harry Dresden has many epic moments in Changes, leading to an intensely awesome climactic final battle, with Crowning Moments of Awesome for multiple characters, which ends with him destroying the entire freaking red court of vampires. How does he die, though? After the battle, while he is relaxing on his brother's ship, he gets shot by a sniper and dies before he can react at all. He got better. Also, when we learn the context for the shooting in the next book, it changes from this to a Thanatos Gambit - he orchestrates a Mercy Kill with Jared Kincaid to prevent himself from becoming Mab's servant. He fails.
The death of Annalina Aldurren in the last book of the Sword of Truth series seems particularly mean spirited. After trying (in vain) to convince another character to do something that everyone else in the book had just finished deciding was a bad idea, she gets a hole blasted through her chest, and the killers go so far as to destroy her body so nobody would know what happened. Later on, the man who had in previous books admitted he loved her, after briefly mourning, is seen with a couple of young women in his arms.
In the final book of The Dark Tower series, several main characters die suddenly and anticlimactically, but the one that angered fans the most was actually a villain: The Man in Black (aka Randall Flagg, who has appeared several of King's novels). After being built up as a character of incredible intelligence, cunning and mysterious power for seven books straight (not to mention being Roland's nemesis), he makes a random appearance in the last book and is killed off quickly and suddenly by Mordred.
Also, Sheemie Ruiz. Several mentions are made of how one more teleport would kill him by brain aneurysm, the reader is led to expect some Heroic Sacrifice on his part... and what happens to him? He cuts his foot on a piece of glass and dies of blood poisoning on his way to safety.
In Tom Clancy's The Bear and the Dragon, Robby Jackson has become Jack Ryan's Vice President, and therefore the first black VP of the United States. Either this was too controversial or Clancy needed an excuse to bring Strawman Liberal Ed Kealty back, because in Teeth of the Tiger, Jackson has been assassinated by white supremacists completely offscreen and with no more than a passing mention in the novel itself.
Inverted in The Last Battle. The (previously major) character of Susan does not appear, and is abruptly dismissed within a couple of paragraphs as having had an offscreen change of character, causing a lot of fan resentment. The inversion comes when it turns out that she's the only major character who isn't dead, everyone else having died in a train crash and therefore being eligible to enter the Narnian afterlife.
Also in an earlier book, a minor villain is crushed when a tree is hit by lightning and falls on him, though this may or may not have been an act of StarClan. Amusingly the tree is subsequently used as a bridge, making the trope name extremely literal.
Arthur Conan Doyle's stab at killing off Sherlock Holmes might not have caused such a massive fan revolt if he hadn't gone to such pains to make it clear that even if he hadn't killed him off, he wouldn't have any more stories to write - no, not even from Watson's old files.
The death of Tiger Cub in the second Night Watch book is narrated by an enemy and consists of only slightly more than "So I killed her." Justified, since he barely knew her, but the readers did.
She is barely mentioned later, when Anton takes over as the narrator, despite being good friends with her.
Done very intentionally in Gormenghast with Fuchsia, who is one of the most sympathetic and developed characters in the story, present since the very beginning of the first book. She falls out of a window and dies.
Due to the Loads and Loads of Characters in the BattleTech fiction, this was bound to happen at some point. Notable examples include Hanse Davion in the early days of the Clan invasion, Knight in Shining Armor Arden Sortek towards the end of the Civil War, and more than a few major characters from prior novels in the course of the Word of Blake Jihad, including mercenary commanders Jamie Wolf, Wayne Waco, and Daniel Allard.
If you pay attention to the Blood of Kerensky novels, he had been showing signs of heart trouble, and had died of heart failure at the end of the last of the trilogy. A more apt choice would be Morgan Hasek-Davion in the Twilight of the Clans series, who was assassinated with poisoned whiskey while en route to Huntress and the assassin's employer, to this date, still has not been discovered. To make it more egregious, said employer must have been grasping a new toy: the VillainousIdiot Ball! Since the only two groups (Word of Blake and Katrina Steiner) who could possibly have motive/opportunity to kill him would be Inner Sphere factions, and thus, I don't know, would want to keep one of the best generals in the Inner Sphere alive to stop the Clans?
The chronologically first two books of Alexander Kent's "Richard Bolitho" Wooden Ships and Iron Men series showed Bolitho as a midshipman developing a close friendship with another middie. And then in the next book published, newly-promoted Lieutenant Bolitho comes aboard his newest ship and explains his gloom: "My best friend was killed a month back." The death isn't treated lightly, but it wasn't for another 26 years that Kent wrote a book showing how it happened.
Merrick gets an entire The Vampire Chronicles book dedicated to her character and transition from a human to a vampire, only for it to end with Merrick deciding to end her life in order to help a spirit "Go Into the Light."
In The Worm Ouroboros (one of the earliest fantasy novels ever) Lord Gro, a major and probably the most complex character in the book, dies abruptly in the Battle of Carcë. His death is treated very curtly and feels decidedly anticlimactic.
In Star Wars: The Old Republic: Revan, the Exile is unceremoniously backstabbed.
If you think about it, Lord Scourge is slightly justified in that. After his Force Vision revealing that The Emperor will not be slain by the three of them, he decides to save his own skin by "revealing" himself to have been The Mole. So he kills Meetra and gets Revan captured.
Sisterhood Series by Fern Michaels: Three big ones end up happening in the first 7 books. The first one is the fate of Julia Webster, who has AIDS and is dying from it. After the book Payback, she is sent to Switzerland to undergo experimental treatment. She seems to get better, but by the book The Jury, she has a stroke (it is debatable if a stroke is related to AIDS), seems to recover from it, but then passes away without letting any of the Vigilantes visit her! The second one is the fate of Nikki's partner Jenny, who was hit by a drunk trucker and killed off, along with her unborn child in The Jury! The third one is the fate of the Barringtons, a family of criminals who treated horses as profit-making machines and let a number of them starve to death. They appeared in The Jury, but they ran off and vanished before the Vigilantes could go after them. Then, in the book Free Fall, when Nikki asks for an update on the Barringtons, Charles reveals that they are dead. They were located somewhere in Europe, driving a car at a high speed, crashed it, and went up in one mighty fireball of an explosion. Fortunately, the Barringtons were bad guys, so there is little reason to shed tears over them!
In Tolkien's The Silmarillion, Elu Thingol's death is pretty anticlimatic compared to the other Elves of his stature. While they die in blazes of glory Thingol... gets ganked by some dwarves when he refuses to pay them for some work. Tolkien apparently wasn't satisfied with this end, but never got around to changing it.
General Scott Dixon, the hero and protagonist of many of Harold Coyle's war novels, is killed off suddenly and rather unceremoniously in the book Cat and Mouse when his helicopter is shot down out of the blue by some terrorists. There isn't even an actual death scene written for him. Just a scene where Dixon's son Nathan is informed of his father's death. The actual death itself occurred off screen (or off page anyway). Now, granted, Scott Dixon was getting pretty old at this point, and it made sense for Nathan to stop living in his father's shadow and become the new protagonist. But still, considering all the previous novels with Scott as the hero and the off-handed manner at which he died, this definitely counts as a "Dropped a Bridge on Him".
DomDaniel simply, suprprisingly and unceremoniously disappears after his bones were consumed by Spit Fyre in Queste.
Ditto for Jillie Djinn in Darke, who expires standing up on Marcia's sofa a moment after the climax, without getting much attention.
Twilight: James, the Big Bad of the first book, corners Bella and prepares to rip her to shreds, but then Edward and the rest of the Cullens arrive. Just when you were expecting some epic combat, Bella blacks out, and since she's the narrator, the next scene shows her in the hospital, where Edward reveals that James is dead. Er, where's the action? Where's the epic combat? Where's the one part where something interesting could have happened? GONE!
This also happens to Laurent in the second book. His entire presence in the book goes: he corners Bella in the meadow she hung out with Edward in in the first book, the werewolves show up and chase him off, and it's later mentioned that they killed him.
Axis by Robert Charles Wilson takes place about 30 years after Spin. The protagonist Tyler Dupree (from whose viewpoint Spin is narrated) is hardly mentioned in the sequel. We only get to meet his widow Diane, who mentions the death of her husband rather off-handedly. In fact, it's all the more jarring because Tyler is known to have become a Fourth (a human with an extended lifespan), so 30 years should not have been enough for him to die of old age. Also Ibu Ina, a secondary character, although that is more justified as she was never made into a Fourth.
At the end of the book, Diane literally gets a building dropped on her and refuses to have her consciousness be "saved" by the Hypotheticals.
In the Paladin of Shadows book Choosers of the Slain, this happens to Mikhail, who gets unceremoniously gunned down without a proper death scene after we've been with him for nearly the whole book.
In Virginia Woolf's To the Lighthouse, we are famously told in an abrupt parenthetical aside during an interlude between the book's two majors sections that the novel's central character, Mrs. Ramsay, "died in her sleep the night before." In The Waves, a minor character dies falling off a horse midway through the book, and the six POV characters spend the rest of the book obsessing over it.
Larry Niven's Ringworld ends with three of the main characters escaping from the titular structure along with a new Love Interest for Louis named Halrloprillalar Hotrufan (or "Prill" for short) choosing to come with him to escape the Ringworld for civilized Earth after spending thousands of years among savages. The sequel The Ringworld Engineers picks up about 20 years later. Louis is suffering partly because the government has hidden away Prill from the galaxy and forbidden him from seeing her. He's then kidnapped by a Pierson's Puppeteer, who claims that his agents have located Prill and are recovering her. However, that turns out to be a lie on the agents' part. Prill has been dead for 18 years, when boosterspice (a life-extention drug meant for humans) accelerates her aging process. She brought some of her people's version of the drug (a much more potent version), but it was confiscated.
Most of the characters who die in Dale Brown novels get to die in combat. Jon Masters, on the other hand, suffers the ignominy of dying to a car bomb.
Wheel of Time: Shaidar Haran disappeared from the story around the time Robert Jordan died. In A Memory of Light, Rand finds his boneless corpse lying in the middle of the Bore right before he starts fighting Moridin; Moridin refers to him as a pawn of the Dark One, and leaves it at that. For reference, he was a Myrdraal capable of wielding the One Power, and was so terrifying that even the Forsaken tried to stay on his good side.
Mort: The Duke of Sto Helit, a major antagonist, dies in an offhand way near the end when his hourglass happens to be one of the ones Death accidentally broke during his fight with Mort.
Protector of the Small: After spending three and a half books as Keladry's primary antagonist (sort of The Face for Tortallan misogyny) and threatening that she will need to watch her back once they're both knights, Joren of Stone Mountain is abruptly killed by the Chamber of the Ordeal. The Scanran war takes over the book almost immediately after he is disposed of.
The titular Julian is in big trouble, as his enemy Constantius has the biggest army in the world, and his legions are deserting him. Then Constantius dies of a fever, naming him as heir, just like he did in real life.