Predating Chuck by nearly half a century, Joan Hardy (Julie Haydon) appears as a member of the Hardy family in the first Andy Hardy movie, A Family Affair in 1937, and plays a bigger role in the plot than Andy. She disappears without explanation for the remainder of the long-running movie series.
In the Disney movie A Goofy Movie, Roxanne is shown to be Goofy's son Max's love interest. In the sequel, An Extremely Goofy Movie, Roxanne and her best friend Stacey (Max's friend Bobby's love interest) never appear and are not mentioned, despite all the trouble Max went on that summer. Roxanne does appear in an episode of House of Mouse, though. Meanwhile, A Goofy Movie itself removed Pete's wife, Peg and PJ's sister, Pistol along with both the family pets, Chainsaw and Waffles, from Goof Troop, without even a passing mention of any of them in either movie, and with a line in the sequel that explicitly proves Pistol's not around anymore.
Transformers: Age of Extinction does this to the entire human cast from the first three movies along with most of the surviving Transformers from the previous movie. However, the latter could be attributed to the actions of Cemetery Wind in the period between the two movies.
The original Transformers: The Movie does this to some of the surviving cast members up to that point, as nearly anyone who didn't die or was implicitly shown to have survived is never mentioned again.
Shortly after Unicron transforms Megatron into Galvatron, Skywarp and Bombshell are transformed into the identical "Cyclonus and his Armada", however, the "Armada" (which is just one guy) is never seen or mentioned after this scene. It is disputed who got reformatted into Cyclonus and who into the Armada. Bombshell is the one shown in front and Skywarp further at the back so it is considered that Bombshell got formatted into Cyclonus however. Skywarp is the major character and much more loyal to Megatron (Bombshell and the other insecticons consider them seperate from the other Decepticons) and has the personality of becoming Galvatron's/Megatron's new Number Two.
If you look closely, whenever Snarl is present, one of the other Dinobots is missing. And the script even refers to "the four Dinobots". It's like the entire production team thought there were only four of them and couldn't decide which four there were.
Nightcrawler was a major character and love interest for Storm in X2: X-Men United, but didn't even appear in X-Men: The Last Stand because actor Alan Cumming found the make-up and prosthetic process grueling and refused to return to it without Bryan Singer. Cumming can be seen in the behind-the-scenes footage for X2 already stating that he never wants to go through the ordeal again. The video game based on the films which takes place between the two movies explains that Nightcrawler, a peaceful man, went abroad to distance himself from the X-Men's violent lifestyle.
Poor Riptide. He goes from No Name Given in the previous film to not even earning a mention in X-Men: Days of Future Past. Particularly notable since Erik takes the time to list all the characters not in this movie because they died in between films. Though it can easily be assumed that Trask killed Riptide along with the others, he still goes unmentioned.
Dr. Dolittle: Rodney the guinea pig is nowhere to be found come the sequel, probably because his voice actor, Chris Rock, declined to return. While Rodney may likely have died of age by Dr. Dolittle 2, this is never addressed at any point.
In the early Olsen-banden movies, Kjeld and Yvonne had two children: A son Børge and a smaller daughter. As the series went on Børge became an important regular while his sister vanished into thin air.
At least in the Norwegian versions, Kjell had two sons and a baby daughter in the first movie, and while the middle son Basse becomes a regular character, the other two have disappeared completely by the second one. Likewise, Benny ends up fathering a kid during the first movie, but both kid and fiance are never again referred to, and the only supporting cast member to reappear is Hansen the bartender. After movie 2, he's gone too.
In the animated version of Charlotte's Web Jeffrey the gosling, Wilbur's best friend besides Charlotte, is never seen again after he attempts to join Wilbur, Charlotte, and Templeton in the crate and is taken out.
In The NeverEnding Story III, Atreyu — who the co-protagonist of the first film and a major character as Bastian's best friend in the second — is nowhere to be seen. The very noticeable actor changes for both Atreyu and Bastian between each film create a lot of dissonance anyway.
American Pie and American Pie 2 center around four friends; Jim, Kevin, Finch, and Oz. In American Wedding, Oz is completely left out. You'd think they'd at least mention why one of Jim's best friends didn't attend his wedding. He returns for Reunion though.
In Eddie and the Cruisers, Frank Ridgeway plays a key role in the band and the story. When the sequel comes out, there's no mention of Ridgeway at all. They even go so far as to replace Frank's image with Sal in recycled footage from the first film.
At the end of Legally Blonde, Elle becomes best friends with Vivian Kensington, her rival for her boyfriend. However, in the sequel, Vivian is never even mentioned.
In Halloweentown, Luke was a fairly important character, and he became even more important in the first sequel. He disappears completely in the third and fourth films, just in time for Marnie to get a cuter, human Love Interest instead.
In Weekend at Bernie's II, Catherine Mary Stewart's character disappears without a mention, even after one of the heroes spent the entire first movie romantically obsessing over her.
Shenzi, Banzai and Ed failed to appear as well, although they are mentioned to have fled from Pride Lands following the first film. They also made several appearences in the 1995 Timon & Pumbaa series.
In the Direct-to-Video sequels to An American Tail, Bridget, the love interest of Fievel's older friend Tony Toponi, vanishes without even a mention and Tony starts lusting after other women. This could possibly be because Bridget's voice actress was terminally ill when the movies were made and died soon after (for their faults, the 3rd and 4th films did manage to get most of the original voice talents from the first two movies). It could also have been because the writers wanted Tony to be single so he could interact with Fievel more.
In Batman Returns, Catwoman, Batman's love interest and villain throughout most of the movie, is last seen on the roof of a building before the movie ends, and is never seen again in the two subsequent films (and is only mentioned once, and in a subtle way, when Chase Meridian says "Or do I need skintight vinyl and a whip?"). Michelle Pfeiffer was meant to get her own film as Catwoman, but the project fell into Development Hell and eventually crawled out in 2004 with Halle Berry as the star and nothing to do with the Burton films.
According to Batman Wikia, Catwoman was suppose to appear in the then planned second sequel directed by Tim Burton, but Warner Bros considered Burtonís dark toned-movies to be difficult to sell to young audiences, so the project was then passed to Schumacher. We know what happened.
Crabbe disappears from Harry Potter and the Deathly Hallows Part 2, when he always appeared alongside Goyle in all of the first six films. Although the filmmakers had a reason for cutting him out (his actor was arrested for drug possession), no mention is given to him at all, Harry never asks where he is, and Malfoy doesn't seem to notice, as he specifically gets Goyle and Blaise Zabini (another Slytherin ally in the books) when he Apparates into the dungeons. Crabbe was supposed to die in this movie too, but due to the character omission they killed off Goyle instead.
Parvati Patil, who does not appear alongside Padma in the last film (who was seen less in the series than Parvati).
Viktor Krum, Cornelius Fudge and Buckbeak, among others. While they're not exactly main characters in the books after their main plotlines end, they do appear in later books. In the films, on the other hand, they're not even mentioned after they've gone.
Some of the Hogwarts ghosts didn't make it past the first film. Nearly Headless Nick managed to stick around a little bit longer and was last seen in the second film. Moaning Myrtle disappears after the fourth film. Colin Creevey has a sizable role in the second film and is then never seen again. He's sort-of replaced by Canon Foreigner Nigel. Madam Hooch is only in the first movie (this was due to a conflict with the actor). The Fat Lady is never seen after the third movie and that appearance was a case of The Other Darrin.
What's particularly odd about the Colin/Nigel situation is that when there are pictures of Nigel in companion media, he's often referred to as 'Colin Creevey'.
The entirety of Slytherin house with the exception of Draco, Crabbe, and Goyle might as well be extras as far as the movies are concerned, Viktor Krum can be assumed to just be back home as far as the movies are concerned, Rita Skeeter was important in one scene and can be assumed to be getting on with her career. Played straight with Fudge and Buckbeak though.
Barty Crouch Jr. who was Spared by the Adaptation, yet never appears in any of the later movies. In the book, he got his soul sucked out by the Dementor's Kiss. The film merely states he will be sent back to Azkaban. In later movies, Voldemort frees all of the Death Eaters from Azkaban yet Crouch Jr. never appears alongside any of them. True Chuck Cunningham Syndrome indeed.
Blade gave us Karen Jenson, a haematologist who develops a biochemical weapon against vampires and even finds a freakin' cure for vampirism. The movie ends on the note that, if she wants to be useful, she'll have to make Blade a better serum to suppress his bloodthirst. She never shows up or is mentioned in the sequels, but Blade doesn't have any serum-related problems (so presumably she did make him a better one), and other characters are mentioned as being cured of vampirism.
In the first Men in Black movie we're told that K was in love with his old girlfriend throughout his career and his original partner was D. In the third movie, J time travels back to the early years of K's career. K is shown to be romantically interested in O and there's no mention of his old girlfriend or D.
In High School Musical, during the "Stick to the Status Quo" musical number, three characters decide to follow after Troy and confess their Hidden Depths: a member of the school's basketball team bakes, a smart girl dances hip-hop, and a skater boy plays the cello. While the first two, Zeke Baylor and Martha Cox, become major supporting characters, the skater boy is never seen or mentioned again once the song is done.
The Dark Knight Rises: Due to Heath Ledger'sdeath, the Joker is not released by Bane with all of Gotham's other prisoners. People are 90% certain that he would have played Scarecrow's role in the plot, were the actor still alive.
The Novelization explains that he is kept in the otherwise abandoned Arkham Asylum, its sole inmate, and Bane never got around to releasing him.
The Police Academy franchise has a nasty case of the syndrome with characters disappearing between each of the sequels:
Their First Assignment: Cadet Leslie Barbara, Cadet Karen Thompson, and Cadet George Martín.
Back in Training: Capt. Pete Lassard and Sgt. Vinnie Schtulman.
Citizens on Patrol: Cmdnt. Mauser, Sgt. Kyle Blankes, Mrs. Fackler, Cadet Hedges, and Cadet Karen Adams.
Significant characters from the Disney Fairies franchise frequently fall victim to this when the next movie comes along. Some of the lucky ones are Demotedto Extra but others have simply disappeared without explanation by the next installment even though they had top billing right below Tinker Bell in the previous film.