The X-Files: "X-Cops" (which was shot as an episode of the show COPS), "Post-Modern Prometheus" (black and white), "Jose Chung's 'From Outer Space'" (told through conflicting flashbacks), "Bad Blood" (also told in conflicting flashbacks), "Triangle" (split-screen), and "Humbug" (first comedy episode).
One of the biggest offenders being The Drew Carey Show having April Fools Day episodes, live episodes, and the like.
An episode of Married... with Children called "Top of the Heap," which focused on the Verduccis (Al's friend, Charlie, and Charlie's dim-witted son), and aside from a brief appearance by Al (both in the beginning and in the end when he takes back the TV he lost in a bet, featured none of the regular characters.
Another pilot-in-disguise episode was "Radio Free Trumaine." It featured a pair of radio jockeys at Bud's college, with only minor appearances from Bud and Kelly and major appearances from Steve (who is now Trumaine University's Dean of Students) and Marcy (who is leading a protest against the radio station).
Another Poorly Disguised Pilot episode called "Enemies," which focused on Kelly, her new boyfriend, and her new boyfriend's sarcastic friends.
Other examples from Buffy the Vampire Slayer include "Hush" where nobody speaks for most of the episode, "Restless", which takes place mostly in the characters' dreams, and "Superstar" where an extremely minor character usurps main character status, even taking over the opening credits.
There was also "Conversations With Dead People," which features five stories taking place in different places at the same time, each of which includes, well, a conversation with a dead person. The stories weren't even thematically linked until the next episode, when they all converged.
And the group amnesia episode - Angel had one too.
"The Body" was probably the best example. It begins immediately where the last episode ended, with Buffy finding her mother's pale, lifeless body on the couch, and except for the last five minutes features nothing supernatural, just the poignant shock of an entirely normal, unexpected death. The effect is heightened by the complete lack of background music, close-ups of seemingly random details, etc.
Also, the episode "The Zeppo", which took place entirely from Xander's perspective
And don't forget "Smile Time", wherein the basic formula is the same, except the main antagonists are puppets, and Angel himself becomes a puppet for the duration of the episode.
The Millennium episode "Somehow, Satan Got Behind Me" featured four demons sitting in a coffee shop discussing humanity's flaws; the main character of the series only appeared for brief periods. Many fans of the series consider the episode a favorite.
Scrubs had a few episodes following this. "My Musical" was, of course, a musical. The episode "My Life in Four Cameras" becomes a typical Sitcom. Also, to a lesser extent, the "His/Her Story" episodes, as they're narrated by different characters than normal.
There was also "My Day Off", where JD had to experience the hospital as a patient, not a doctor.
And "My Princess" in which the events of the episode are portrayed as a fairytale being told by Doctor Cox to his son.
NewsRadio had two episodes which, while not actually changing the format of the show or the characterization of the leads, instead changed the setting (by way of a clever set redress). The characters act as if nothing is different. The 3rd season finale was set on a radio station in space, and the 4th season finale was set on the Titanic, and roughly followed the plot of the hit 1997 film. These episodes, naturally, do not follow series continuity, especially since both involve the deaths of nearly all of the main characters.
Law & Order: Special Victims Unit, episode "Gone". The episode literally begins with the arrest and preliminary hearing of two suspects, but soon a twist is thrown in. The audience is caught up to speed when the ADA asks the detectives to tell her again all the details of the case. Pretty much the entire episode deals with the legal side of things.
The My Name Is Earl episodes "Y2K" (which, in flashback, deals with the characters' experiences at the turn of the millenium) and "Our "Cops" Is On" (most of which is presented as an episode of COPS featuring the characters).
And don't forget "Our Other "Cops" Is On".
Doctor Who has had a few of these, including the new series' "Doctor-lite" episodes, made because the actors playing the Doctor and his assistant don't have the time to film 45 minutes of footage for all 14. So we get an episode with the main characters reduced to a few, usually crucial, minutes of screen time that they could film in a day or less.
In the original series, "Mission to the Unknown" did not feature any of the cast, who did not get a mention. The episode concerned some humans' doomed struggle against Daleks on an alien planet and acted as an episode-long prologue to "The Daleks' Master Plan", which aired a few weeks later.
Series 4 gave us the Donna-lite episode "Midnight" and Donna-centric Doctor-lite episode "Turn Left", which were filmed at the same time with different crews and casts and both unusually dark stories. Donna only has about one minute of screentime in "Midnight" and the same is true for the Doctor in "Turn Left."
The Series 3 episode "42", which had the normal cast, took place in Real Time.
The "Deadly Assassin" 4th Doctor story was the first and only Doctor Who arc to not include a companion.
The penultimate episode of House's first season, "Three Stories", takes the form of a lecture that Gregory House gives to medical students. He narrates three case histories, absurdly embellished to the point where one patient is "played" by Carmen Electra. As House's own memories intrude, it turns out that Carmen Electra is actually House himself, in a flashback to his infarction.
Season two had an episode called "The Mistake" where Stacy investigates what caused the death of a patient. The patient storyline is told mainly through (sometimes conflicting) flashbacks.
The wonderfully irreverent Lois and Clark did this quite frequently. The episode "Don't Tug On Superman's Cape" is a collection of TV pastiches revolving around Supes and Lois' relationship troubles, with a hamtacular Jonathan Frakes providing the B-story/frame story of the episode.
Homicide: Life on the Street did one of these practically every year, with some stand-outs being Night of the Dead Living, Three Men and Adena, Colors and The Subway.
The Law & Order episode "Aftershock" was a famous episode that showed the main characters on their day off from work, having attended an execution of a criminal the night before, culminating in Claire Kincaid getting Killed Off for Real in a drunk driving accident.
Also of note, was "Marathon", another episode which famously followed Briscoe and Logan spending a twenty-four hour period dealing with a variety of cases, with the prosecution team appearing only briefly. The episode was popular enough that the writers did a sequel several years later, with Briscoe and Green and is one of those "translated" into Law & Order: UK (an honor Dick Wolf reserved for his favorite and/or what he felt were his best episodes of the original).
ER,much like Homicide, would do one every year, starting with Love's Labor Lost and including memorable episodes such as Hell and High Water, The Long Way Around and Secrets and Lies, a Breakfast Club type episode where the doctors sit around and just talk to each other.
Star Trek: The Next Generation had "Family," which took place on Earth and featured the crew members seeking out their families while Picard dealt with the emotional trauma of his recent assimilation and clashed with his wine-making brother.
That season also featured "Data's Day", a Day In The Life episode centering on Data.
Supernatural's third season featured a Sam-and-Dean-lite episode, "Ghostfacers," which focused on two characters from the first season episode "Hell House". It was also shot like a real pilot, with handheld cameras and everything. Demonstrates one of the dangers of these episodes in that it did not look like an episode of Supernatural and, combined with the confusion due to the writers' strike and a lack of advertising, many people didn't realise they were watching the right programme. And switched off.
In fact, Supernatural does so quite frequently (the episode "Monster Movie" comes to mind). It is one of the (many) reasons the show is a firm two-thirds in Deconstructor Fleet territory.
Coupling did this enough so that it practically became the norm. Episode quirks include the following: One told first from the point of view of Jeff talking to an Israeli woman who speaks no English, which then switched to an Israeli perspective where the Hebrew dialogue is in English, the English dialogue is in gibberish, and we find out what she's really saying; One that takes place entirely in a split-screen perspective after a break-up, where one-half of the screen is devoted to each member of the break-up; And the one that narrates the same nine and a half minutes from three different perspectives.
Jimmy Olsen's Day In The Lime Light episodes on Smallville have been taking on a style like this. "Noir" was a Film Noir parody, and the most recent was done in the style of a spy thriller. Fans have noted they are some of the weakest episodes in the series.
The Monkees: "The Monkees on Tour" (a cinema verite documentary about the actual band playing a live show); "The Monkees in Paris" (basically a longform music video of the guys romping around Paris and getting chased by gorgeous models); "Fairy Tale" (a Fractured Fairy Tale with cardboard cutout sets and props.)
The West Wing had the seventh season episode "The Debate", which was a real time presidential debate between Santos and Vinick shot in one take. It was pretty freaking amazing.
Not just in one take, but done twice - once for live broadcast on the East Coast, and once for live broadcast on the West Coast.
In addition, the fifth season episode "Access" was a mock documentary of Press Secretary C. J. Cregg. It was not great.
Murder, She Wrote, especially in the later years, had multiple "Jessica-light" episodes focusing on recurring characters (e.g. reformed Gentleman Thief Dennis Stanton; MI6 agent Michael Hagarty) or supposedly based on one of Jessica's books.
One episode, "The Days Dwindle Down", was essentially a follow-up of an obscure film noir thriller "Strange Bargain", with members of the movie's original cast reprising their roles as Jessica investigates the 35-year-old murder.
An episode of The Father Dowling Mysteries, which was partly told by a "fictionalised" version of events set in the 1920s. (So when Father Dowling was visited by yuppified gangsters in sharp suits, his fictional counterpart was visited by stereotyped hoods in double-breasted pinstripes.)
Yet another episode featured Dowling doubting his deductive powers when the police arrest the wrong man on his reasoning. This doubt causes him to congure up a consulting detective...none other than Sherlock Holmes.
Stargate SG-1 did "200", their 200th anniversary episode, a humorous episode that's basically about SG-1 sitting around the table while trying to come up with a good movie idea.
The Day in the Limelight episode of CSI Las Vegas, "Lab Rats". The whole episode takes place inside the laboratory, focusing on a group of lab technicians revisiting the miniature killer case, the main investigator team making only short appearances, and the whole atmosphere being a lot more humorous.
"Lost and Found in Translation" (Dino Thunder) had the Rangers watching a Japanese TV show based on their exploits (actually a Hong Kong Dubbed episode of its source series Abaranger)
"And... Action!" (RPM) was a behind-the-scenes episode.
Bones: The season four finale is a Dream Sequence in which Booth and Bones are married and running a bar, with most of the cast working for them.
The season eight episode "The Ghost in the Machine" is shot entirely from the perspective of the skull of the person whose death Booth, Brennan and the Jeffersonian team were investigating.
The Fringe episode "Brown Betty" is mostly the story that Walter tells to Olivia's niece, in which Olivia is a Private Detective in a pastiche, dealing with variations on the shows characters. Who occasionaly sing.
Criminal Minds usually has the team trying to hunt down a Serial Killer. Episodes that did something different include "Secrets and Lies" (the team searches for a mole in the CIA headquarters), "Honor Among Thieves" (the team investigates a kidnapping perpetrated by the Russian mafia), "Derailed" and "Minimal Loss" (the team become embroiled in a hostage situation), "Lessons Learned" (the team go to question a terrorist), "Masterpiece" (the killer turns himself in at the beginning), "Tabula Rasa" (the team help prosecute a killer) and to a lesser extent "True Night" (like a regular episode, except the killer is the main character).
There have been a few of these in Home and Away's 2010 season. One such occurrence was an episode themed around dreams (Annie had some dreams of Romeo that involved nudity, Tony and Rachel had dreams about how they weren't prepared to care for Harry). Another occurrence was an arc where Miles gained an imaginary friend who turned out to be an aged-up ghost of his daughter, complete with psychic ability.
Monty Python's Flying Circus itself has the Cycling Tour episode, which is unique in Pythonian terms since it actually has a continuous and more or less coherent plot.
Community would provide several examples of this if it weren't for the fact that, at this point, doing this pretty much is its general formula.
For this reason, it could be argued that the show itself is Something Completely Different, because unlike pretty much every other show out there, it doesn't have any discernible formula except for its lack of any discernible formula.
The Thirty Rock episode "Queen of Jordan" was done entirely in the format of a Bravo reality show.
LOST had a few of these episodes. The first was "The Other 48 Days" which, instead of featuring one character with off-island flashbacks, focused on all the characters from the tail section of the plane, and told the story of their time on the island.
Each season of the Masters Of Horror anthology (usually set in modern day Everytown, America) had one episode set in the early 19th century and another filmed in Japan and directed by a Japanese actor.
The Farscape episode "Revenging Angel" features repeated excursions into the psyche of the comatose John Crichton...in the form of pitch-perfect Looney Tunes parody animations. That's weird enough, but when the slapstick and cartoon logic start to cross over into live-action sections it all gets a bit brain-breaking. And horrific. They blew up D'Argo!
The How I Met Your Mother episode "Symphony of Illumination" used the Framing Device of Robin talking to her kids in the future, rather than every single other episode's framework of Ted talking to his kids. However, it turned out that all the narration and the kids were figments of Robin's imagination while she was reflecting on the events of the episode, and Future Ted actually was telling the whole story in the end, making the episode an imagine-spot-within-a-framing-device-within-a-story-within-a-framing-device.
The Prisoner had a couple of episodes that were way out of their Village context, only resolved at the end - "The Girl Who Was Death" shows Number Six as a secret agent out in the outside world in a loopy story that turns out to be a bedtime story he's telling children in a Village nursery. "Living in Harmony" is a straight Western (casual viewers could easily assume they tuned in to the wrong show) until the ending where it was all a mind control experiment.
The Charlene Tilton episode from season six (with musical guest Todd Rundgren and Prince before he hit it big with 1999 and Purple Rain) had a running storyline called "Who Shot C.R.?" (a take on Dallas's "Who Shot J.R.?" storyline) with Charles Rocket (a.k.a "C.R.") falling in love with host Charlene Tilton, and the other cast members vowing revenge. Rocket ends up getting shot during a sketch called "After Midnight" about two swingers who trade sexual innuendo while bathing a dog. At the end, he unintentionally shocks the audience when he says, "I'd like to know who the fuck did it?" and, thus, brought the maligned Jean Doumanian-era to an end.
The season eleven episode hosted by George Wendt with Francis Ford Coppola also had a running storyline, only this time, it was about Francis Ford Coppola trying to make Saturday Night Live more cinematic and worth watching (as its ratings at the time were in the toilet). It failed miserably.
The two episodes that started on a more dramatic tone after a tragedy (the Reese Witherspoon episode that came on after the 9/11 attacks, featuring Mayor Rudolph Giuliani and New York City's fire, police, and medical departments; and the Martin Short Christmas episode from season 38 that came on a day after the Sandy Hook Elementary School shooting that started with the New York City Kids' Choir singing Silent Night).
The season three episode on December 17, 1977 is the first (and only) episode hosted by someone who isn't a celebrity. An old woman named Miskel Spillman was chosen to host an episode as part of a contest SNL had where an average viewer wins the chance to host an episode.
The first episodes of seasons seven and ten are the only ones that have no host. James Caan was originally supposed to host the season seven premiere, but had to back out after his sister was sent to the hospital for bone marrow cancer. For season ten, Ebersol chose not to have a host.
The central McGuffin of Person of Interest is the Machine, a government surveillance supercomputer that can predict acts of terrorism. Most episodes focus on Reese and Finch, who take advantage of a side-effect of the Machine to help ordinary people that are about to be involved in a violent crime, but the episode "Relevance" unfolds from the perspective of Shaw, a government agent whose job is to follow up on the Machine's primary function of trying to stop terrorists, and winds up becoming one of the people Reese and Finch have to help. While Reese and Finch do appear, it's only for about five minutes.
Friends had the 1-hour special "The One that Could Have Been." Aside from the pre-opening sequence, the entire episode takes place in an alternate timeline where each member of the gang's lives had turned out differently than in the actual show (although things more or less wind up close to how things are regularly by the end).