Jeff in American Dad! was accidentally kidnapped by aliens when he got shoved into their ship's tractor beam that was meant for Roger. He disappeared for the next several episodes until he was rescued from Roger's home planet in the 150th episode, "Lost in Space."
Miss Lilly from Angelina Ballerina was nowhere to be seen in the sequel series The Next Steps outside of a picture of her at Angelina's school and the occasional mentioning of her name. Likely justified in that her voice actress Judi Dench is a well-known character actress and hiring her to reprise her role would be very costly.
Buster Baxter went on a year long trip around the world with his dad whom he doesn't spend much time with since he and his mom are divorced; he returns in the season opener.
In a Very Special Episode dealing with a fire in the school, Mr. Morris left for New Mexico after recovering from injuries sustained in said fire. He has since appeared in Postcards From Buster. Strangely, he—-or someone who looks like him—-has made background appearences from time to time at Lakewood Elementary. However, the real Mr. Morris seems to be about to finally make a return.
Happens regularly in Avatar: The Last Airbender. Minor characters such as Haru, Jet and his Freedom Fighters, Suki, the Mechanist and others are introduced in one episode, never mentioned or seen again until half a season or more later, pop up for one more episode, and disappear again. The series finale managed to bring back everyone (who hadn't died) in a group shot, except for the handful that were put on a Long Bus Trip.
In Blue's Clues, to help its impressionable young viewers cope more easily with the resignation of host Steve Burns, he supposedly leaves to go to college and is quickly replaced by a brother, Joe.
The Care Bears cousins suffered this fate in the early 90s due to Kenner revamping the line. Those that weren't put on the bus were transformed into bears. The bus briefly came back in 2003, only to leave again in 2005, owing to a failed attempt by Play Along Toys to reintroduce the cousins, but at least four of the cousins are now permanently back off the bus as of November 2015.
William Dunbar gets put on a very interesting (and painful) sort of bus. After being attacked and possessed by XANA on his first mission as a Lyoko Warrior, he's effectively put out of commission for the entire season. He does return, but only just in time for the series to end two episodes later. There's no real explanation as to why this happened, though he was dislikeda bit. He returned for Code Lyoko: Evolution.
Kiwi, on the other hand, got on the bus for Code Lyoko: Evolution, likely because of the difficulties involved in training and handling a live-action dog, but it is said that his disappearance will be explained later in the series.
Ed, Edd n Eddy: Jib was literally put on a bus by the end of the only episode he's "appeared" in.
Timmy Turner's fairy dog Sparky has suffered this fate in The Fairly OddParents!. After having proven largely unpopular with fans since his introduction at the start of Season 9 owing to his obnoxious personality, Sparky has thus far been entirely absent in Season 10 without any given explanation onscreen. Word of God confirms that Nickelodeon elected to drop Sparky from the main cast after he failed to win over audiences, meaning that the bus is not likely to return to Dimmsdale with its four-legged passenger anytime soon.
To make matters worse, Cousin Oliver Poof also suffered this fate as well since he barely makes appearances in Seasons 9 & 10.
Family Guy has had some. Parodied in "A Lot Going On Upstairs" by having several recurring characters including Fouadnote the foreign sarcasm guy sidelined backstage in Stewie's dream.
Gargoyles is sort of an inversion: the World Tour Arc has Goliath, Elisa and Bronx leave New York for a huge chunk of the season, and they're the ones we mostly follow. As such, the rest of the clan and the New York cast only appear in two Day in the Limelight episodes.
Harvey Birdman, Attorney at Law takes this to the extreme by having the character, Phil Sebben, not only be put on a bus, but be hit by one as well, only to return driving the bus himself BACKWARDS, across North America and under water no less, then runs over Harvey with it thus putting the entire show on the bus. "HA HA HAAAA! Final episode stunt casting!"
The Season 2 opener of Iron Man saw Force Works disbanding and Hawkeye, Century, and Scarlet Witch all resigning. Only War Machine and Spider-Woman remained by Iron Man's side for most of the second season, though the others came back for the final episode.
Justice League features a perfect example of this trope in its second season finale when Hawkgirl resigns from the Justice League and flies off to go soul searching. Sure enough, she returns at the end of season three when she discovers Solomon Grundy may have come back from the dead.
More permanently done with A.M.A.Z.O, who's still out on the edge of the universe trying to figure out how to beat Solomon Grundy. Word of God was he would return in the last episode as a Brick Joke, but they forgot about him.
Little Miss Calamity disappeared offscreen in Season 2 of The Mr. Men Show. The official explanation was that Chorion, the production company behind the show, didn't like her. She did manage a cameo as a statue in the second season.
Princess Luna nearly suffered Chuck Cunningham Syndrome when she vanished after the second episode, and was never seen or even mentioned again in the season. However, she returns in the fourth episode of Season 2.
The background pony Derpy vanished as well due to a scandal, also believed to have gotten Chuck Cunningham Syndrome, but returned at the end of Season 3 and has a role in an episode of Season 4.
Gilda the Griffon stormed out of Ponyville after a falling-out with her childhood friend Rainbow Dash in early first season, and never showed up again. But then came Season 5...
Trixie likewise left after humiliating herself early in a Season 1 episode, and didn't return until the third season.
Twist was introduced in "Call of the Cutie", and seen briefly in a few episodes, such as "The Return of Harmony Part 1" , "The Cutie Pox", "Hearts and Hooves Day" and "Twilight Time", and hasn't had speaking roles ever since. Her voice actress, Alexandra Carter, moved from Vancouver to Philadelphia around the time Season 2 was starting, so it's unlikely that she'll return.
Babs Seed seemed to be set up for more appearances following her introduction and reappearance in Apple Family Reunion. However she hasn't been seen since the third season even though, like Queen Chrysalis, she made more appearances in the comic book. The fact Babs got her Cutie Mark off screen in "Bloom and Gloom" makes things look even more worse.
After The Golden Oak Library got destroyed Twilight is seen cuddling Owlowiscius only for Owlowiscious to fly off to who knows where. He eventually returns halfway into Season 5.
Ms. Bellum was phased out of The Powerpuff Girls (2016) at the end of her only appearance in the episode "Bye Bye, Bellum", taking a long vacation after her years of working non-stop. Word of God is that "Ms. Bellum wasn't quite indicative of the kind of message we wanted to be giving out", which is vague but probably has to do with her being Ms. Fanservice.
The Regular Show episode "The Real Thomas" ends with Thomas being phased out of the show
Their original other neighbours, The Winfields (who appear in the long character-packed "pan" sequence during the intro, suggesting they were perhaps originally intended to have a larger role in the series), relocated themselves to Florida in Season Four, to be replaced by Ruth Powers and her daughter (though Mrs. Winfield does show up again in a crowd scene in "Lisa the Iconoclast"). Ruth herself disappeared shortly after two appearances, and in her third appearance in season 14 ("The Strong Arms of the Ma") Marge calls her "my old neighbor," indicating she too eventually moved away.
Homer's half-brother Herb hasn't been seen since season three, after he regained his fortune with a baby translator. Homer even lampshades to Herb as "his seldomly seen half brother". Believe it or not but Herb has a line in a season 24 episode. Homer, suddenly concerned about the kids' requirement for a legal guardian in the event of his and Marge's untimely demise, calls up his brother, only for Herb to say, "I'm poor again." D'oh!
Homer's rarely seen third friend, after Lenny and Carl, at the nuclear power plant, Charlie, disappeared in Season 5's "The Last Temptation of Homer". He was sucked up a giant tube, similar to Matt Groening's later Futurama, after complaining to Mr Burns.
Nelson's two "weasels," who play a large role in the Season 1 episode "Bart the General" basically disappear after that one; many seasons later it's revealed they moved to Shelbyville.
The Smurfs: Most of the other Smurfs that didn't get lost in time in Season 9's first three episodes, as there was no return home episode that was even produced or aired.
Chef had a bridge dropped on him after his voice actor left, but the ending allowed for the possibility of a return by making him "Darth Chef" (although Isaac Haye's death would obviously require The Other Darrin).
He did returns briefly in South Park: The Stick of Truth as a nazi zombie. Just as the others are starting to knock some sense back into him. Clyde sets his corpse on fire.
Officer Barbrady was put on a bus at the end of "Toilet Paper", announcing that after the ordeal of solving the toilet-papering of a teacher's house he needs to take a long vacation. By the next episode to involve police, "Li'l Crimestoppers", Barbrady has been replaced by an actual police department, though he has still shown up from time to time.
When Space Goofs returned for a second season, Stereo was absent, apart from a couple guest appearances. He's not even in the intro where they're shown crashing into Earth. This also contradicts the theme song, which states, "Five little monsters were riding through space..." as there are now four.
SpongeBob SquarePants: Recurring characters Mermaid Man and Barnacle Boy made their last speaking roles in "Patrick-Man!", which aired three months after the former's voice actor Ernest Borgnine passed away. The latter's actor Tim Conway would follow suit in passing seven years later. With both voice actors gone, the two characters' appearances have been relegated to non-speaking cameos since said episode, and it's unclear what the future has in store for both characters.
Steven Universe has a long and proud history of this, usually coupled with The Bus Came Back. Jasper and Lapis were trapped under the ocean as Malachite for an entire season, Peridot was left flying around the Earth for about half a season, Jasper (after returning from being fused) was turned into a mindless corrupted Gem monster and put into a bubble, and after being sent on a wild-goose chase, the Rubies were left floating in the void of space. And in Season 5, Lapis takes the barn into space to flee from the wrath of the Great Diamond Authority.
Characters have a nasty habit of this happening to them in Thomas & Friends, especially in the HIT Entertainment era (2002-present). Among the classic characters who have been gone for many seasons (not counting one-off characters like Billy and Bertram who were only created for marketing purposes, and Bulstrode, who was only intended to appear for one episode) include Duke, Boco, Caroline , Old Slow Coach, Neville, Dennis, Molly, Hector, Arthur, Murdoch, Mighty Mac, and "Fearless" Freddie,
Fortunately, in Season 17 and the special King of The Railway, The Bus Came Back for several characters thanks to the new writing team, who have set out to save the show from the Seasonal Rot it has endured since 2004. King of the Railway saw the return of Jack the Front Loader (from the cancelled spin-off Jack and the Pack), while Season 17 brought back fan-favorites Duck and Bill & Ben, as well as Harvey. Season 18 marked the comeback of Oliver and his brakevan Toad, as well as Duncan, Oliver & Alfie from The Pack , Daisy , and the Scottish Twins Donald and Douglas. While season 19 brought no body back, Season 20 brought back Trevor , Max , Monty and Rosie. More characters that have been put on a bus are likely to come back.
In the Big World! Big Adventures! series (Season 22 onwards), Edward and Henry leave the main cast and are replaced by two new female characters, Nia (an orange tank engine from Kenya) and Rebecca (a large yellow streamlined engine).
Also in Big World! Big Adventures!, the narrator is replaced by Thomas talking to the audience. Mark Moraghan (who had narrated since Season 17) still plans to remain in the series in another capacity, such as making the switch to a voice acting role, as well as taking over from the late Ben Forster in the YouTube storytime segments.
Bulgy and Terrence would eventually return in Season 21
Most of the characters on Timon & Pumbaa who had reappeared over the course of the first two seasons (Speedy, the Vulture Police, and Timon's meerkat friend Fred) failed to appear in the 1999 season, on which the series is generally regarded to have jumped the shark.
When Toonami came back, TOM 4 was subjected to this as a new version of TOM 3, TOM 3.5, was the host. However, TOM 4 did make a cameo talking to TOM 3/5. Then was subjected to a Bus Crash as The Intruderreturns and proceeds to gloat about adding TOM 4 to his body count.
Total Drama does this about every new season, leaving old characters behind and bringing back more popular ones or ones that were eliminated early on to give them a fresh start. But when Chris says that once a contestant is gone from a season, and they "can't come back, ev-er," he doesn't always mean it.
With the exception of Izzy, Ezekiel, and Owen, All-Stars was the first season in which non-competing characters didn't appear at all even in cameos.
Mike of the 2nd Generation cast suffered from this after All-Stars. According to Word of God the controversy around how his MPD was portrayed in that season has lead to him not appearing in any future seasons.
Transformers Animated has a rather weird use of the bus. At the end of the third season opener "Transwarped" Sari is shut down by Ratchet in a desperate attempt to keep her over-upgraded body from destroying both herself and the city. Not only did she not appear for the next four episodes, no one even seemed to think about her — including her own father.
As of "Human Error" she's back off the bus, now taller, more mature, and able to make blue balls of floating electric... stuff. The coma hasn't been mentioned again.
Ultra Magnus was also put on the bus in season 3. If by 'bus' we mean the ICU.
And in perhaps the most terrifying way to be sent packing on the bus, Shockwave stuffs Blurr into a bus by force. More specifically, Blurr is crushed into a cube and shipped to oblivion. And it is implied that Blurr survived.
Transformers: Prime has Airachnid, who after one of many rivalry battles with Arcee is accidentally trapped in a stasis pod. Team Prime decide it's a good idea to bring her back to base, but now 6 episodes later is never mentioned again. Considering the fandom's huge hatred of her it's clear to see why.
She eventually reappeared in season three, still trapped in her stasis field on the Decepticon warship. A Dark Energon fueled Sylus broke her out of containment, but Soundwave immediately Space Bridged her and the remaining Insecticons to a desolate moon of Cybertrons, where she presumably died of starvation.
In the original The Transformers, dozens of characters were put on the bus, a result of the writers and animators not having knowledge of the 1986 Movie (which hadn't yet aired in Japan).
Jazz was technically put on a bus, because although the character survives the movie and makes 2 cameos, his voice actor, Scatman Crothers fell ill and later died.
Many of Casey Kasem's characters were put on buses. (the supercomputer Teletran-I was Put on a Bus to Hell.) Autobot headquarters (the Autobots' stranded-on-Earth spacecraft and Teletran-I inside of it) were buried when Trypticon smashed the mountain it was lodged in. Cliffjumper, like Jazz, survived Unicron, but fell off the vocal map after 1 cameo by the character. Bluestreak was never seen after the 1986 movie's Battle of Autobot City. All of this stems from Kasem's displeasure with stories featuring a stereotypical Middle Eastern dictator and his country, "Carbombya".
Many of the Season 1 and 2 characters were either killed off in storyboards (but not in the finished product) or never mentioned again, only to turn up as cameos late in Season 3, or in Japanese audience only spin-offs. Hound turns up in Transformers: Headmasters
Tigatron and Airazor went off to scout the extent of the Vok's damage to the planet at the start of the second series of Beast Wars to make room for the Fuzors. When they returned, they ended up being abducted by the Vok, and would not return until partway through series 3.
Phil Coulson leaves for a special mission at the start of Ultimate Spider-Man Season 3, only showing up in cameos in a handful of episodes. Taken Up to Eleven in the fourth and final season, where Coulson doesn't appear at all, even in the Grand Finale.
Triana Orpheus from The Venture Bros. left the Venture Compound in order to study magic with her mother.
Triana has been seen again - she was Dean's date to their home-school prom.
World of Winx: Every character from Alfea, Cloud Tower, and Red Fountain from the original Winx Club has been put on a bus. Save for a brief reference, not even the Specialists appear in the new show.