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.
As this is very common in horror movies, Scary Movie makes fun of this by having Charlie Sheen's character from the third movie die in the first scene of the fourth via giant erection. Brenda from the first two Scary Movies also dies in the first and early in the third, but since she seems to die a lot and come back it doesn't really count.
The 1980s version of the second The Hills Have Eyes movie did this to Ruby, the mutant girl who survived the first film, by smashing her head in with a rock.
The third X-Men film possibly did this in regards to Cyclops, because James Marsden had to go work on Superman Returns.
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.
The protagonists of the second and third movies are also implied to be dead by newspaper clippings. With the three survivors of the fourth movie being killed in the end, it's clear that whoever survives in the movie will die eventually.
At the beginning of Alien³, the Sulaco launches an escape pod which lands on a planet. Newt and Hicks are both killed in gruesome ways (the gory aftermath is shown), while Bishop has one scene in which he asks to be turned off.
Interestingly, 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.
Part 3's Kristen was killed in Part 4 (along with the rest of her Dream Warriors team).
Subverted with "Dream Master" Alice, Freddy's strongest adversary, who survived not one but two films (Parts 4 and 5).
Alice was not his strongest adversary, Nancy was. Only she had the strength of will to take back her energy from Freddy making him useless, which she couldn't do in the third film because he was feeding off the new generation, not her. By the end she was physically and mentally exhausted by taking care of 3 kids who couldn't last 5 minutes without her as proven in the 4th movie where each one goes down without a fight.
In Damien The 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.
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.
Keep in mind that this is also her fate in the books.
Mathis from Casino Royale fare a little better than the norm, making it about halfway through Quantum of Solace before being gunned down and tossed into a dumpster.
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.
Hostel Part II: Paxton, the Final Guy from the first film, is decapitated early on.
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 3 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. Saw IV saw the death of two characters who were introduced in Saw II, Det. Eric Matthews and Agent Daniel Rigg. The main character of III, Jeff Denlon, was also quickly dispatched. Special Agents Peter Strahm and Lindsay Perez were introduced in IV and died in the second Saw film they appeared, respectively V and VI, the second one after having been declared dead in V, in which also their boss, Agent Erickson, who first appears in V, ended up dying. Detective David Tapp, whose fate is unclear in I, is revealed to be dead in V and his fate is shown in the canonical ending of The Video Game, while the saga could possibly avert the trope with the return of the 'possibly' lone survivor of I, Dr. Lawrence Gordon, for the last sequel, VII, and/or playing it straight with the return of some survivors of other movies who will be in VII (it's been confirmed that Simone and Emily from VI will be back too).
Vin Diesel's character 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 Genre Savvy 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.
What's really interesting is that Vin Diesel is going to be returning as Xander Cage in xXx: The Return of Xander Cage. The title seems to make it clear that the film will not be a Continuity Reboot. It looks to treat Xander's death as Canon Discontinuity or a Re Write in which he survives.
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, and his wife Adrian dies of breast cancer prior to part 6.
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.
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.
It's implied in the first sneak preview for Fast and Furious 7during Han's graveside service that Hobbs will buy the farm against Ian Shaw beforehand.
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.