By those rules, Hill’s character from Law & Order does not count. That show usually gave departing characters more of a sendoff than a throwaway line in the first episode of the next season.
The OP specified “characters you liked.” Although it was satisfying to see him show up on a milk carton.
Married with Children’s first season featured Luke Ventura, a sly and handsome womanizer who was Al’s co-worker. (“The day Luke Ventura can’t help a friend is the day he has something better to do!”) Ultimately, he had disappeared by season two.
Dr. Marvin Monroe of The Simpsons was seen less and less until he vanished for good, later being revealed to have died offscreen. (In reality, Harry Shearer hated doing his voice.)
Yeah!! Gendry!
Also from Game of Thrones: Ser Ilyn Payne was written out of the series by season two, despite having a much larger presence in the books. The reason was because the actor was gravely ill with cancer – however, thanks to radical surgery, he did survive and is currently cancer-free. Unfortunately, the producers don’t seem keen on bringing back his character; he doesn’t even appear on Arya’s death list anymore.
In the books, Rickon Stark (youngest of the Winterfell brood) was effectively Chuck Cunningham’d by book two, sent off to distant lands and never heard from again. However, in the HBO series, he does return…
…and promptly gets murdered.
He didn’t die. In one episode he revealed he was “just very sick.” Total retcon, yes.
That’s Dr. Feelgood’s guitarist. Cancer in 2013, still going strong thankfully.
Rickon will probably eventually be back in the books. Part of the problem is that his part of the world wasn’t mentioned except in passing in book 4.
Patty (the non-Pepperminty one) and her friend Violet from Peanuts.
In the series My Three Sons the original eldest son, Mike, married and “moved out of state” with his new wife on the first episode of Season 6. He was never seen again (he may have been mentioned from time to time, but he was gone.) The series lasted another 6 seasons.
Shermy got Chuck Cunningham’d even earlier. I can’t say I really missed any of them.
The Gumps, a successful comic of the 1920s, mentioned in the very first strip that the had a daughter in college and a son in the army.
They were never mentioned again.
If comic strips are allowable, then Bloom County had a few characters that got jettisoned:
Bobbi Harlow was Milo and Binkley’s feminist schoolteacher, who date Cutter John and was perpetually fending off Steve Dallas’ harassment.
Yaz Pistachio was Opus’ fiancee, who broke up with him during the ceremony and never appeared again.
There was an scuzzball ex-convict Limekiller who appeared for a while, until Berke Breathed realized that Bill the Cat was a much funnier scuzzball character.
There was also a crooked politician character who was always being caught up in scandal situations.
On TV, Donna from That 70s Show originally had two sisters, at least one of them did show up onscreen, but neither one was ever mentioned again after the first season. More significantly, Eric’s sister vanished without a trace (after marrying Fez so he could stay in the country.)
Including Milo’s grandfather, who was hardly ever seen after the first year or two.
Is this different from Mandyville? I guess the writing was on the wall, as CJ blocks her from going into a meeting in the Oval Office, but after that…she’s just gone.
Ainsley Hayes was Mandyvilled too…although I think hers was closer to moving to Miami. 
True, but I never liked him. 
I, too, came into this thread to mention Valerie and Tina Pinciotti. Also, Edna Hyde.
So has this thread degenerated into an indiscriminate list of every character who was ever Chucked? 'Cause out of the ones posted so far that I recognize, none of them seem particularly memorable to me, and nobody seems to be explaining why they miss them so much.
Bea Bendaderet from “Petticoat Junction.”
In real life, the actress was suffering from lung cancer, and missed a number of eps in Season 5. She was well enough to return for the last ep of the season.
She was in the first half dozen or so eps of season six, and her last on-screen appearance lasts for about 10 seconds, in which she goes to Steve and Betty Jo’s house to check on Betty Jo (expected to go into labor soon), who is with the Doctor. She is holding a towel for some reason, speaks briefly to Steve, then rushes into the bedroom and disappears.
The next ep, in which the baby is born, has a stand-in for Benaderet, but she did record her own lines so that they could be dubbed.
She was briefly mentioned in passing once or twice, but that was it.
Personal opinion: If she was so sick that she couldn’t work any longer, you surely couldn’t tell it from her last appearance. She might have appeared to have lost some weight (and that might account for why she was holding the towel), but I thought she still looked pretty good, and not sick at all. I’d be interested in hearing what any of the cast had to say about what it was like in real life, because she hid it well.
The train engineers in “Petticoat Junction” had similar appearances and disappearances without explanation. (Rufe Davis, Smiley Burnette, Byron Foulger.)
Al Harrington in “Hawaii Five-O.” Just suddenly appeared, and just as suddenly disappeared. Same with Kono (Zulu).
IIRC, he wasn’t Chucked. In his last episode, he had gotten a job in California, and Ann and the girls were making plans to move out there with him, until he told Ann that he wanted to have a child with her, she flat-out refused, and they broke up.
There was a second character on Happy Days who was Chucked: “Sticks,” the show’s one main black character, who was briefly the drummer in Richie / Potsie / Ralph’s band (eventually, Chachi took over, and Sticks was never spoken of again.)
And if “babies who were announced but never born” count, I think there was one on Petticoat Junction; at the end of the next-to-last season, the new doctor (June Lockhart’s character) is about to leave for New York when she decides to stay after she examines Betty Jo and discovers she’s pregnant again, but that pregnancy is never mentioned again.
Eric’s sister was played by a different actress (Christina Moore) for that story line because the original actress (Lisa Robin Kelly) had developed a drug problem.
Also Lyman, Odie’s original owner, from the Garfield strip.
That was mine. Maybe they shouldn’t count. I missed one element of the Chuck-ness requirement. While they unseen babies were characters who “2)disappears 3)without explanation and 4)without being referenced once absent” they never were “1)recurring characters”. And we never got to like them (from the OP).
actually I don’t know about the strip but the second Garfield animated series that ran for a few years on cartoon network/boomerang solved that …jon said he disappeared in a rainforest and he was never seen again
he became a sort of wildlife vigilante protecting a rainforest he came across …he was injured and found this guy who helped him was using a local monster legend to scare off developers when the guy moved on he took over …
how odie found out was it showed the monster on a tv show bigfoot footage style he recognized and they ran off to save him
And speaking of Bea Benaderet, did they ever mention Jethro’s mother on Beverly Hillbillies after Bea got her own show?