Played for Drama in Attack on Titan with the death of Marco. He's killed off-screen without anyone knowing how he died, without the slightest semblance of dignity or glory. This shocks Jean to his core, and his greatest fear becomes dying a non-heroic death and having his bones be thrown and burned in an anonymous pile just like Marco's were. This drives his Character Development, as he not only wants to make sure that his death, should it come, is warranted, but he also doesn't want to let down Marco's high opinion of him. It is later revealed how Marco died, and while it does have a bit more plot significance than it initially lets on, it still stands as an inglorious way to die.
Despite being a fairly central character and being connected to several plot threads, it's later mentioned that Ymir was killed offscreen for her Titan Power.
Although Ginga: Nagareboshi Gin manages to make most of its deaths impressive in one way or another, the manga-only wolf arc manages to make some exceptions:
Suiga's death, being taken into a pool of lava by one of Gaia'sChild Soldiers, seems rather quick and unimpressive by the series' standards. Made all the worse by the fact that his comrades pay next to no attention to his death due to Akame getting tackled into the crater next... and surviving by using his ninja skills.
Mahou Sensei Negima!: In the Gecko Ending of the first anime series, Negi's father Nagi, the legendary "Thousand Master", for whom Negi has been searching the entire series (and most of his life), is casually disposed of by shoving him through a dimensional portal so that Negi can get to the real business of the show's Grand Finale, which is retconning the bridge dropping of another character.
Wolf's Rain did something similar in the four OVA episodes that conclude the series. Remember, the wolves were trying to get to Paradise, and the series up to that point had suggested they had a chance of making it — so the first time one of the wolves died it was especially shocking.
Then again, the ending confirmed that they couldn't have reached Paradise anyway because it doesn't exist — the world is trapped in an endless cycle of death and rebirth and it's the wolves' fate to initiate every rebirth.
Vanessa Rene in Madlax is killed off in such an anti-climactic way that some viewers haven't even realized she is dead until another character starts burying her. Madlax is shown to grieve over her though, which makes it even more puzzling why in the end she runs off with the woman who killed her.
Vanessa's death may better fit a Heroic Sacrifice or Taking the Bullet. The foundations were well set up in the proceeding episodes, it is definitely a very in-character sacrifice and not an arbitrary, collapsing bridge in the jungle. True, she didn't expect to die ... but her belief doesn't make it an unrealistic turn of events. She put herself in front of a sniper's bullet. She then earned her heartwarming reward, to be reunited in spirit with her Mother and Father ... pretty much making it clear she didn't miraculously survive the shot.
In the end of the first arc of Groove Adventure RAVE, the protagonist's father dies shielding him with his own body from falling rocks. That would be heart-warming, if not for the fact that said father and son have always exhibited superhuman levels of strength and endurance, and also the traditional feats seen in Anime. A bridge was definitely dropped here.
And let's not get started on the deaths of Arukenimon and Mummymon.
In the movie, Big Agumon (as he's called in the end credits) literally gets a bridge dropped on him, allowing him to digivolve into Greymon - a minute or two later he and Parrotmon are destroyed in his own attack.
A bit of irony in 02's case: by Digimon Adventure tri., nearly all of the Chosen save for Hikari and Takeru are trounced in a fight with Imperialdramon at the start of Reunion. There has been no trace of Daisuke and the group in the movies since.
Orochimaru from Naruto gets the shaft so badly that a bridge is dropped on him twice. First he is killed in a relatively brief fight with Sasuke, and his own mind-control power meant to aid him in taking over Sasuke's body gets turned on him and he ends up being absorbed into Sasuke's mind. Later on, when Sasuke is fighting Itachi, he gets his chakra drained which "frees" Orochimaru...only for Itachi to seal him in a permanent, inescapable genjutsu before he can do anything. Subverted later because he comes back.
Way before him, Dosu was suddenly killed when he tried to take out Gaara between stages of the exam and happened to have attacked him when the Shukaku was in control.
Directly afterward, a second bridge is dropped on Chunin proctor, Hayate Gekko, who saw it happened, heard Kabuto and Baki talking about the invasion, and was killed off by Baki right there with almost no build up. His girlfriend in the ANBU ops was among those who found the body. She swears revenge on his killer and is promptly Brother Chucked.
Also Tailed Beast hosts besides Naruto, Gaara, and Yagura (who was dead before the series started). One was introduced for the sole purpose of being beaten, one was just shown defeated, and 3 of them were killed off off-screen (it wasn't until the author drew a group picture that we even saw what the hosts for the missing ones looked like)...
After Naruto and Killer Bee had Kurama and Gyuki extracted from them. While everybody is rushing to save Naruto, Bee hasn't been seen since.
Konan's fight was made pointless. When it was revealed that her exploiting his weakness was made irrelevant after he could use Izanami by sacrificing a pointlessly covered eye.
In Ashita no Nadja, Miss Applefield, who gets a shelf dropped on her off-screen as she performs a Diving Save to protect one of the orphan kids. This serves no other in-story purpose than having her Orphanage of Love disbanded and giving Nadja yet another reason to angst.
And another one is how Jose gets hit by a carriage right after he and Carmen have resolved to separate but stay in friendly terms until they truly reach their dreams.
JoJo's Bizarre Adventure: Speedwagon and Stroheim die in part 2's epilogue from black lung disease and Germany's invasion of Russia respectively, with only off-handed mentions. In Part 5, Narancia is killed off-screen by Diavolo. Later on, Part 6 takes this to the extreme with Pucci using Made in Heaven to drop a bridge on the entire universe, rebooting the series.
Zoids features a number of these, possibly the most infamous in episode 13 of Zoids: Fuzors. The climactic, three-way battle between the Liger Zero Phoenix, the Buster Fury and the Matrix Dragon (the latter which had been hyped as one of the most powerful Zoids ever just an episode prior) ends with the Buster Fury and the Matrix Dragon getting shot in the back by the Energy Liger. As a final indignity, the Berserk Fury and the Buster Eagle are seen in the following episode looking better than they did after they'd been shot, but being declared as "damaged beyond repair, no good even for scrap." What? (Made even more inane when you remember this is a Merchandise-Driven series, and the sole reason Buster Fury is being written out is to be replaced by the Gairyuki.)
Although a major side-villain and somewhat expected to die at some time during the series run, Full Metal Panic!'s Seina quite literally does have one dropped on her. By her own brother. The Behemoth's activation causes the structural supports for the warehouse to collapse around the main cast during their escape, including the water-filled room Seina is hanging onto a rail in. But we don't get to see that right then. Instead we see her about to shoot Andrey Kalinin despite the fact he came back for her. We see the gun go off as a cliffhanger to episode 11. In episode 12, we see Kalinin alive and Seina mortally wounded. In a flashback we then see her hit by a large girder which caused the gun to go off. That was pretty darned random.
Leonard's death is quite anti-climactic. He's the major villain of the latter half of the entire series,so you'd expect an epic mecha battle between him and Sousuke. Wrong! Kalinin merely shoots him because he's not ending the world fast enough. No big deal.
In the final episode of The Big O, a side-villain named Vera gets into a Megadeus bigger than any other in the series, and gives a big, dramatic speech about how she will unleash a curse upon the city. Then, a beam breaks off of the mysterious giant stage lights over the city and falls on them. It is not acknowledged by the characters who witnessed it. The show must go on.
This scene made about as much sense as anything else that happened in the course of that episode, which was either a Gecko Ending, a Gainax Ending or a bit of both depending who you ask.
In Soul Eater, South American Death Scythe, Tezca Tlipoca seemingly dies this way. Although nobody knows if it'll stay this way.
Nah, he replaced himself at the last second.
And he seems to have died again just seven chapters later. Although this time it seems to be for real, although it seems like way less of a bridge drop this time around since it not only got some fanfare, but the whole chapter devoted to the fight that ends this way. He's techincally still alive.
In the movie version of AKIRA, Kaori suddenly meets her end when a mutating Testuo accidentally pulls her in and she's crushed by his insides. Her death in the manga was more plot-relevant, as she's shot to death by Tetsuo's treacherous lieutenant and perishes in Tetsuo's arms.
Word of God says this was originally not the case. Izumi had a completely written scene, her Tear Jerker death, but it was written out of the script. Her voice actress was even apologized too, for making her have no lines
In Sailor Moon the last three of the Witches 5 get very anti-climactic deaths. Each of them is killed within one episode - Tellu is destroyed by her own plant monster, Viluy is killed by her own nano-machines and Cyprine gets tricked into killing herself. In contrast Eudial and Mimette got long-running arcs leading up to their eventual deaths.
In Sailor Moon Crystal, the shitennou aren't killed one after the other and stay alive together long enough for the senshis to free them of their brainwashing...only to be killed in the next scene by an energy wave sent by the arc's big bad.
In Murasakiiro no Qualia Yukari is written off quite suddenly in an unexpected manner, considering her importance until then. She dies off screen in unknown circumstances.
Happens in Xam'd: Lost Memories with Rival Turned Evil Furuichi. He's had his big fight with Akiyuki and Haru, his childhood friends and two of the show's heroes, and now it looks like he's finally made his peace with their being together and going to mend fences with them—only for the soldiers to catch up to him and arrest him for being a Xam'd, at which point he succumbs so deeply to despair that he tears off his own head! What makes this all the worse is that Furuichi is one of only a small handful of characters in Xam'd to die at all, and none of his former friends seem to care that he's gone—in fact, we never even see his mother's reaction to his death!
Fairy Tail, a series marked for its habit of teasing character deaths and then not following through, abruptly kills off every government head in one swoop at the start of the Tartarus arc. An explosion mid-meeting kills Lahar and all or the councilors save Org, who is the killed several pages later.
Mobile Suit Gundam SEED Destiny has YunaRomaSeiran tricked into returning control of Orb to Cagalli when she reappears during Operation Fury when Orb is overwhelmed and on the back foot. Arrested for treason, they attempt to interrogate him to no avail. Yuna manages to escape from his captors when a Mobile Suit fight distracts them for a moment, but not seconds later, a GOUF Ignited is shot down in front of him and squashes him like a bug. If he'd just stayed put and kept complaining, he would have lived, but instead he's killed by the needless war he started.
In the world of One Piece, where people seem to be able to survive about anything (including gunshots, explosions to the face, losing thrice the amount of blood a human body even contains, getting building thrown onto them, being poisoned to death, getting impaled, getting eletrocuted by millions of volts), Zoro's childhoodfriend Kuina dies an extremely anticlimatic death. While all other Straw Hats usually have a tragic backstory with a person in their past heroically sacrificing themselves, or dying an epic death, Kuina dies by falling down some stairs.
Chapter 36 in Fuuka ends with the title character very suddenly being run over by a truck and killed. Turns out the title was actually referring to a different Fuuka.
In Joker Game, two characters gain prominence in the first two episodes: Lt. Sakuma and a particularly clever and adept-seeming spy, Miyoshi, who appears to be on the way to becoming the former's foil. However, Sakuma vanishes from the story after that, the series reveals itself to be episodic, and the next time Miyoshi is shown, he's been killed while on a mission and doesn't even have any lines in his own focus episode. He's the only D Agency spy to die during the course of the series.
Yuusha ga Shinda starts out in this manner, with the legendary hero dying by falling into a very obvious spiked pit trap (complete with a chunk of pork as bait). Then the villagers bury the body in an unmarked grave and pretend he was never there, just to avoid further trouble. Later, the protagonist (the guy who set up the trap to begin with) plans to defeat the demon lord in the exact same way.