Cotton Weary, a non-main character from the Scream series who helped Sidney in the second movie (despite the fact that she mistakenly sent him to jail about a year before the first) and killed the Big Bad, died in the first 10 minutes of the third movie to enforce one of the "rules" of a threequel: In the third movie all bets are off and Anyone Can Die. Randy, the horror movie buff who identified all the tropes in the first Scream (1996), gets killed halfway through Scream 2, though he is Genre Savvy enough to make a Video Will to dispense some final advice for Scream 3.
Phil Coulson had been in three previous movies and featured in the Marvel One-Shots. His actor even got suspicious that he would die once the director (who has a track record for Anyone Can Die shows) called him and said Coulson was "The Heart that unites the superheroes" - which eventually translated to "Loki killing Coulson would propel the Avengers to assemble and fight together". And even if Coulson wound up returning in Agents Of Shield, the fact that he is Back from the Dead is a huge plot point there. Coulson's revival will apparently never be mentioned in future MCU films.
Final Destination's final shot before the credits made it quite clear that the three survivors were going to be down to two. We never saw the freak accident that took out the hero of the first movie. We only got to hear Clear describe it in the sequel who herself almost, but not quite, survived to the credits.
At the beginning of Alien³, the Sulaco launches an escape pod that lands on a planet. Newt and Hicks are both killed in gruesome ways (the gory aftermath is shown), and Bishop has one scene in which he asks to be turned off. The Comic Canon (quite a lot of which was written before 3) sees Hicks and Newt survive, and quite a few fans consider it superior for that reason.
The A Nightmare on Elm Street movies famously had heroines return in sequels only to have them killed off after passing the torch to a new heroine.
Part 1's Nancy was killed in Part 3. Her father dies as well.
Part 3's Kristen was killed in Part 4 (along with the rest of her Dream Warriors team).
Subverted with "Dream Master" Alice, who survived not one but two films (Parts 4 and 5). Her Love Interest Dan plays things straight however, as he survives the climax of 4 only to die early on in 5.
In Damien: Omen II, the old archaeologist from the first movie (played by Leo McKern) who was the only character to know the truth about Damien to survive from the first movie is killed in the opening minutes. In this case, it actually served to wrap up a loose end from the first film.
But how did he get his daggers back? They should have been in an evidence vault somewhere in London, surely.
The character of Doug Masters returns, having not really been dead after all, in Iron Eagle IV. Different actor, though.
In The Godfather Part II, we learn that Peter Clemenza has allegedly died of a heart attack (with Willi Cicci implying he was actually murdered by the Rosato Brothers). Then again, that never caught anyone as a surprise.
In The Godfather Part III, we are told that Tom Hagen died shortly before the beginning of the film. This was done because Robert Duvall refused to reprise the role unless he was paid the same as, or marginally close to, what Al Pacino was getting paid.
Resident Evil: Afterlife killed off all of the Alice clones found at the end of the third film in the first ten minutes.
In Attack of the Clones, Count Dooku can fight both Obi-Wan Kenobi and Anakin Skywalker to a standstill, effortlessly disarms Anakin one-on-one, and he forces Yoda to save Anakin and Obi-Wan so he can run away. In the next movie, he's killed in a duel with Anakin with little fanfare before the introductory action sequence ends to show how much more powerful (and closer to the Dark Side) Anakin has become in the intervening years. Behind the scenes information also suggests that one reason this may have occurred was because Christopher Lee found the fight scenes physically straining due to his advanced age since he was 80 at the time the first film was shot and 83 by the second.
Valentin Zukovsky survives GoldenEye and appears again in The World Is Not Enough where he dies near the end. There were two deleted scenes implying that he actually survived his gunshot wound, but since they are deleted scenes, he seems to be dead canonically.
In Austin Powers: The Spy Who Shagged Me, as a parody of the above James Bond examples, Austin's love interest in the first movie, Vanessa, is revealed to be a fembot and is quickly destroyed. To make the revelation even more absurd, Basil admits that they'd known all along. Austin mourns her death for all of three seconds before realizing he's single again, which makes him so happy it leads to a choreographed dance number. None of this (except for Austin's joy at being single again) makes the least bit of sense, even by Austin Powers standards, but it's not supposed to.
Interestingly enough, Vanessa was meant to continue to be alongside Austin in the plan for the second film, but her actress having scheduling issues meant that this happened.
The character Jake from Rings, a short film that bridges The Ring and The Ring Two, spends the majority of the (surprisingly well-written) story hallucinating and freaking out over the influence of the Cursed Tape. At the end of the horrible seven day-long mind screw, he calls up a girlfriend to pass the curse on to her... He dies in the opening scene of The Ring Two, as the girl refuses to watch the tape and he's pulled into a cheesy special effect.
There's an even better example in the original Japanese works. The protagonist of the first book dies in the sequel, Rasen, and in both the movie sequels (an adaptation of Rasen and an original sequel, Ring 2). In all cases, the cause of death is not being the protagonist anymore.
The Chinese man who originally owned Gizmo returned to reclaim him at the end of the original Gremlins, and dies about ten minutes into the sequel. This, of course, ensures that he is out of the way so Gizmo could end up being reunited with Billy. It's possible that actor Keye Luke was in too poor of health to have an extended role in the film, as he died a year after the film's release.
Welcome To The Doll House, which was very depressing as it was, had a small shred of hope for the tragic main character at the end of the film...until Palindromes was released as a loose sequel. It was revealed that the same main character has committed suicide from depression straight up in the beginning of the sequel.
Whistler dies in the beginning of Blade: Trinity to make room for Blade's super cool new sidekicks, despite the fact that Blade II went to the trouble of resurrecting him after he died in the first film. At least he got a last stand this time.
Saw II revealed that Adam, one of the main characters from the original, had died, showing us his corpse. In Saw III not only showed his death scene (in a flashback) but it also killed off Amanda (a former test subject, then apprentice), Detective Kerry, who had been investigating the Jigsaw case since the beginning and Jigsaw himself.
Special Agents Peter Strahm and Lindsay Perez were introduced in Saw IV and died in the second Saw film they appeared, respectively Saw V and Saw VI, the second one after having been declared dead in V, in which also their boss, Agent Erickson, who first appears in Saw V, ended up dying.
Detective David Tapp, whose fate is unclear in Saw, is revealed to be dead in Saw V and his fate is shown in the canonical ending of the video game.
The saga averted the trope with the return of the lone survivor of Saw, Dr. Lawrence Gordon, for the last sequel, Saw 3D, and also averted with the return of some survivors of other movies like Simone and Emily from Saw VI.
Vin Diesel's character from the first xXx is mentioned in passing as having been killed by a guerrilla ambush in the beginning of xXx: State of the Union, to make way for Ice Cube as the new xXx. Ice Cube is smart enough not to stick around for his turn, and retires at the end of the film so a new xXx can appear in the sequel without requiring his death.
The Director's Cut DVD actually includes a short movie showing the death itself... sort of. Xander is played by Vin Diesel's stunt double, never showing his face, and with dubbed lines from the first film. There's an explosion that apparently leaves behind only a tattooed flap of skin slaps down.
An alternate cut of Highlander: Endgame shows Brenda being hit by a car thanks to the Big Bad of the film, possibly in reference to The Sorcerer.
Wow, Brenda just can't catch a break. Everyone just keeps killing her! No wonder MacLeod always looks so pissed throughout the series.
Connor himself bites it in Highlander: Endgame, when he asks Duncan to behead him and take his power to help defeat the Big Bad. He probably got tired of having Brenda die every time.
Ramirez, Connor's Mentor in the first movie dies halfway through the movie. He's revived in the second, only to die again.
Several major characters have died in the Rocky sequels. Rocky's coach Mickey died of a heart attack in part 3, his former rival turned best friend Apollo Creed is beaten to death by Ivan Drago in part 4, his wife Adrian dies of breast cancer prior to part 6, and Paulie passes away prior to the events of Creed.
Once Upon a Time in Mexico killed off Carolina, the Love Interest from Desperado, in a backstory event that didn't get revealed until the end of the second act of the film. She and Mariachi had a kid before it all went down, which made things extra tragic, since the little girl wasn't spared either. Marquez, the killer and the Dragon for the movie's Big Bad, is Mariachi's main target for revenge during the movie.
A very straight example of this trope is the Bourne Supremacy. Marie, Jason's love interest and a main character in The Bourne Identity, is quickly dispatched during the opening chase.
Kirsty Cotton from the Hellraiser series consistently averts this, after appearing as a character in three movies and as cameos in others. Every time, she gets a little bit craftier at dealing with Hell.
Dimon the Burnt in the sequel to the Russian film Bumer, which is kind of strange considering that his survival is part of what gave the ending to the first film impact.
Bruce Campbell's protagonist in Maniac Cop gets one scene to catch his bearings in Maniac Cop 2 before being killed by the still-living monster cop while reading about himself in the newspaper.
Nancy Allen, who played Officer Ann Lewis in the RoboCop trilogy, is dispatched less than halfway through RoboCop 3, largely due to her own incompetence (she goes to a suspected resistance hideout, which leads to her being gutshot). However, this is because Allen asked the producers to write her character out of the franchise.
Although Tank seemed to be quite fine by the end of The Matrix, the actor's refusal to reprise the role (or leaking details of the plot, according to some) made the Only a Flesh Wound fatal after all.
Marcus also dies between Crusade and Crystal Skull, due to the death of actor Denholm Elliot.
Wilmer Cook in the 1941 classic The Maltese Falcon is arrested (off-screen) by police at the end when Humphrey Bogart calls them. He returns in the comedy sequel, The Black Bird, with George Segal in Bogart's role of Sam Spade; Cook is still in search of the elusive Maltese Falcon but gets killed this time around.
The two final survivors in House of the Dead film are revealed in House of the Dead II: Dead Aim to have died in the interrim. This is something of an unusual example in that the ending of the first film had the guy bring the girl back to life as a semi-zombie using the Big Bad's formula, so even back then you knew things weren't going to end well for the two of them.
Played with in Mission: Impossible – Ghost Protocol where it first appears that the Ethan Hunt's wife Julia from the third film fell victim to this trope. Later it is completely subverted when it is revealed he faked her death to protect her and she is alive and well. She even makes a brief appearance.
Commissioner Loeb is one of the Joker's first major victims in The Dark Knight, while Mayor Garcia is one of the first ones to get killed by Bane in The Dark Knight Rises. Bruce Wayne's love interest Rachel Dawes from Batman Begins also dies in The Dark Knight, but makes it to about the halfway point of the film and her death is a major element of the plot.
Thanks to the Joes' base being destroyed, it's also possible that Ripcord, Scarlett, and the other Joes from the first movie died as well. When asked about it in interviews, Marlon Wayans seemed to suggest his character had indeed been killed off-screen.
Christopher Pike in Star Trek Into Darkness. The man survives being tortured by a crazy, genocidal Romulan (which involved having Veritaserum Slugs shoved down his throat) in the first film, only to get offed by a crazy, genocidal superhuman in the first half-hour of the second film.
Frigga, Thor and Loki's mother and Odin's wife, is murdered by Malekith and Kurse when she refuses to give up the whereabouts of Jane Foster in Thor: The Dark World.
At the end of Machete, Machete and Sartana ride off as a couple. The sequel, Machete Kills, continues from that point but apparently they wanted Machete to be a loner: Sartana is killed five minutes into the movie.
Kick Boxer 2 begins with the protagonist from the first film, getting killed by the villain Tong Po out of anger for losing to him in the kickboxing match, which was the original film's climax. This was done to write Jean-Claude Van Damme (who refused to return) out of the sequel and replace him with Sasha Mitchell, another martial artist slash actor, as the remaining brother in the family out for revenge. Mitchell starred in the next three sequels, but then was unceremoniously killed at the beginning of Kickboxer 5 by a group of henchmen; he was replaced in the movie by Matt Reeves (Mark Dacascos).
Cpt. Esteridge survives The Hitcher but is killed at the very beginning of The Hitcher II: I've been waiting.
The murderous Firefly family makes it through House of 1000 Corpses without a single casualty. Come The Devil's Rejects, Rufus, Mama, Tiny, Otis, Baby, and Captain Spaulding are killed off. Furthermore, Grandpa Hugo apparently passed away offscreen due to the death of his actor and there was a deleted scene featuring the death of Dr. Satan.
Honey Pie falls victim to this in the Feast franchise. She barely manages to survive the first two films, but when the third rolls around and she's looking particularly fierce on the poster◊, she instead meets an early demise within the first 5 minutes or so.
The Subspecies franchise does this when necessary:
Stefan meets an early demise in Bloodstone at Radu's hand.
Michelle's sister, Becky, and Mel who were both protagonists in Bloodstone and Bloodlust meet this fate in the Bloodstorm.The director explained that this was an instance where both actors were too busy to return and the idea to kill the characters originated from a joke passed around on set of the previous two films that he was going to kill them in the fourth film for annoying him on set.
In A Better Tomorrow II, Kit is killed by the main henchman.
Independence Day: Resurgence sees Jasmine and Whitmore die either as a Sacrificial Lamb or Heroic Sacrifice, albeit with the latter's death not happening until the film's climax. Before the events of the movie, Steven Hiller was killed in a training accident, and a supplementary novel states that Constance had died in an accident. Subverted with Julius, who initially appears to die in the tidal wave caused by the mothership's landing, but later turns up alive and well.