In this House thread, it’s dicussed that House is a formula show–patient comes in, House and the Houslings make several wrong diagnoses, finally someone comes up with the right one and they treat it.
The Master of this techique was “Three’s Company”–someone overhears a conversation, misinterprets it, and hilarity ensues.
What others?
Mystery shows like Murder, She Wrote are classic examples - one day somebody’s going to realize that Jessica Fletcher killed all those people.
Ditto certain kinds of lawyer shows, like Matlock or Perry Mason - somebody gets murdered in the first five minutes, it gets solved in the big courtroom showboat reveal.
And of course detective shows like Columbo.
ETA - and if you want to have your medical cake and detect it too, you can hang out with my parents and watch Diagnosis Murder, which I understand actually had a crossover with Matlock - god, can you imagine the nursing home that night?
Mission Impossible. Jim receives secret orders, they review the plan and then complete the assignment.
Law & Order is the absolute pinnacle of this.
Home Improvement is a classic example.
Gilligan’s Island-
Some method/opportunity is discovered to get them off the island. Method/opportunity is lost due to Gilligan’s sheenanigans.
*The A-Team *was famous for this, too. In fact, I remember talking to my boss at the time, back when the show was popular – he was a big A-Team fan. He was busy one night and suddenly realized he was missing the show. He said, “I looked at the clock, and it was 40 minutes past the hour, so I knew I could tune in, see them build the thing that would let them beat the bad guys, and watch the final smackdown.”
There are a lot of shows that lean heavily on their formula.
Friends is another good example. Each episode usually has three short stories and they just bounce between each. Sometimes the times seem odd because it’s night time in someone’s appartment, then it’s day at the coffee shop, then it’s night again.
Scooby Doo:
The gang stumble upon a haunted something-or-other; they investigate; this involves splitting up at some point or other (“Shaggy, you and Scooby go that way; Daphne, Velma, and I will go this way and [del]make out[/del] [del]smoke some weed[/del] search for clues”); Velma loses her glasses, resulting in Magoolike hijinks; Scooby and/or Shaggy is persuaded to take some dangerous action by means of one or more Scooby Snacks; at least one chase scene ensues. They concoct an elaborate scheme to catch the monster, and if it is explained ahead of time how it is supposed to work, something will go wrong, usually because of danger-prone Daphne. The monster is apprehended; they pull off its face; and it is revealed, to everyone’s shock, that it’s really that one guy they met earlier in the episode in a rubber mask and/or using a projector, and the guy explains his attempted scheme, muttering “And I would have gotten away with it, too, if it hadn’t been for these meddling kids!”
Of course, non-fiction shows, like game shows and late-night talk shows, are very often formula-driven.
Monk. “Here’s what happened . . .”
But in spite of the formula, [It is there, I will grant you.], if you miss 5 minutes, or even just one scene of the show, you can turn off the rest of the episode, you’re lost, and you aren’t going to get back on track in time.
It sucks for people like me that have ADD. 
How I met your Mother.
I have caught this show a few times, Only because it comes on after Big Bang Theory.
The small handful of shows I have seen, all seem to work on the following formula:
This is the __________ _________ Again, isn’t it?
Then The narrorator flashes back to when the (Room mates?) tried some process to show someone was wrong about something.
The entire episode effectively brings that “dead” process back from the grave.
Last night (3/30) had an Anti-Bucket List based on things you can not do once you reach a certain age. Things would be added to the list, once someone attempts thing, and fails. The list was edited by everyone, on a need to edit basis.
(All nighters, Eating a large pizza by yourself, Sleeping on a friends futon in his living room. Or Toliet Paper a Laser Tag arena.)
There is another episode that had “Interventions”
The room mates all went to a real intervention of a friend. After that, they started holding interventions on every habit a roommate had, that they didn’t care for.
I saw where this was going:
“Pretty soon, they are going to have an Intervention Intervention”
And they did.
One of the first episodes I remember, the gang was talking about Idiosyncracies that other room mates had, that got on their nerves.
Like, chewing finger nails, or mispronouncing foregin words that English has adopted. Etc.
The would call each person out on it.
There was another one where it boiled down to a game of clue over a sex position + a location + and a famous Canadian Television figure.
Multiple guesses were given as a majority of the gang tried to figure it out.
Multiple guesses are given in one Ep. when someone wants to track down a burgerstand.
**((Previous Life + Past Experience)(Present life + Shared Experiences) Multiple Guesses or Attempts at something) + You cant do that anymore / I bet you I can = How I met your Mother. **
Slight Hijack : Why is the show called that, anyway?
The Addams Family. Someone would show up at the Addams house, goggle at the weirdness, and eventually be unable to take it.
Spider-Man comics of the 1960s: Weird villain would show up, beat Spider-Man and escape. Peter Parker would go through soap opera angst over his personal life. Villain shows up again, but Spider-Man defeats him.
The Millionaire – a down-and-out person is given a million dollars. They find out that money does not bring happiness.
Twilight Zone – something weird is happening. The hero fights against it – but there is a twist at the end!
And at ten of Barney will be sweating
Quincy.
Every week, somebody dies under what look like ordinary circumstances, and the bosses tell Quincy “It’s just a heart atatck. Close the case.”
But he knows better… and he spends days performing every test under the sun, until he proves that the victim was really killed by the Liberal Cause of the Week! In the end, an evil, greedy corporate CEO goes to jail.
Bewitched - To be fair, the first few seasons actually employed some very imaginative writers who concocted interesting stories around the central premise. Eventually though, the series was reduced to the fairly predictable shtick.
-Darren has to make an important presentation to a new client.
-Endora puts a spell on Darren, making him act in some wacky way (or, if Agnes Moorehead wasn’t around, then aunt Clara or Esmerelda would cast a spell that went awry).
-Thanks to the spell, Darren makes a fool of himself at the presentation. Larry gets mad.
-Mrs. Kravitz would see somebody using magic and scream.
-Samantha would reprimand her mother (or Aunt Clara or Esmeralda), and tell her to take the spell off.
-The spell is halted and everything is reverted to normal, just before Gladys can persuade Abner to get out of his chair and look out the window at the Stephens’ house.
-That crazy spell would give Darren a brilliant new marketing idea that he could pitch to the new clients - saving the account. Larry would act like he never threatened to fire Darren.
Quantum Leap.
Sam leaps into the body of someone in order to avert a tragedy by changing history. Only nobody knows what he has to do yet. Eventually, Ziggy figures out what probably has to be done, and Al tells Sam. Eventually, Sam averts the tragedy and leaps into a new body. Oh, boy.
Aren’t all these just simply stating the premise for the shows?
The premise is different from the formula.
Take Eureka for example. The premise is a US Marshall becomes the sheriff for a secluded town full of supergeniuses and highly advanced technology.
The formula is that something goes wildly wrong; it can be a crime, or just weirdness like the sky turning red or something. Carter, the sheriff, begins to investigate, talking to different scientists and trying to understand what could cause the weirdness. An obvious red herring or two is dropped in front of him and he goes after it gleefully, often to much embarrassment. At the last minute, he realizes the real culprit is someone who was briefly introduced at the beginning of the show for something that appeared to be completely unrelated.
The predictability of the formula is the only dark spot in an otherwise fun show.
Some of them are, but House does follow a formula within each episode.
Every episode starts with a character we’ve never seen before collapsing out of the blue. This is our patient. House initially declines the case, saying that it’s a simple case of [some disease/condition]. The person presenting the case gives him one more bit of information that suddenly makes him take an interest in the case. He writes symptoms on a whiteboard and orders a test, but before actually getting the results of the test he orders a treatment. This treatment results in the patient’s heart stopping. The patient is revived. Repeat the previous two steps. Send two doctors to break into the patient’s house. Repeat the steps again. Suddenly a light bulb goes on over House’s head and he solves the case. The patient expresses thanks for the life-saving treatment, conveniently forgetting all of the things they did that nearly killed him. The end.
Edit: I forgot to mention that someone has to say “neoplastic syndrome” during the episode.
The Big Bang Theory has a very simple premise–A pretty woman moves in across the hall from a nerd and a geek.
It doesn’t have a formula. Every episode has a different plot, and some of them are hilarious.