When Jack finds Audrey in 24 season 6, Cheng has tortured her to the brink of insanity. All she says is "Help me, Jack".
Subverted in Agents of S.H.I.E.L.D.: Fitz, who is suffering from severely reduced functioning after the events of the Season 1 finale, continually repeats the phrase "I didn't solve this today" after the team has failed to take down Carl Creel (a superhuman with the ability to turn his body into any substance he touches). It sounds like a Madness Mantra born out of guilt, but it turns out that he's actually trying to say "Something I designed before can solve this", but because of his aphasia, the words aren't coming out right. He only keeps repeating it because no one is getting the message.
After losing her baby thanks to her husband Adam's machinations (desperate to reconcile with her, he held her prisoner while he pleaded his case. The stress of the ordeal sent her into premature labor), All My Children's Gloria spent the next several months babbling either nursery rhymes or Bible verses.
In American Gothic (1995), Merlyn's Madness Mantra was "Someone's at the door". These were her last words as a sane individual. Someone was at the door, and when he came in, he raped Merlyn's mother in front of her.
This same mantra is then used many times over as a Catchphrase for the series, but is especially delicious when employed by Merlyn's ghost to haunt the coroner who lies about her cause of death to protect his family from Buck (complete with the disturbing tape-recording that alternates between extremely fast and high-pitched, and extremely slow and garbled), and later to taunt Buck himself.
In a nonverbal example at the end of season 4, President Clarke commits suicide, leaving behind a note that just read "THE ASCENSION OF THE ORDINARY MAN THE ASCENSION OF THE ORDINARY MAN THE ASCENSION OF THE ORDINARY MAN...". There's a twist in this example, each line has a letter circled, and the circled letters spell "scorched earth"—Clarke had activated the Global Orbital Defense satellites and set them to fire on the Earth and wipe out every man, woman, and child on the entire planet. The Army of Light's fleet took them all out just in time.
"The Corps is the Mother. The Corps is the Father. The Corps is the Mother. The Corps is the Father..."
In Thirdspace after the artifact is found Lyta Alexander writes "There is Danger, Remember" on all available surfaces in her quarters and constantly repeats it under her breath going to the control room.
"Tear the roof off the sucker! Tear the roof off the sucker!" is the mantra of Clarence Cornice, a six-foot six architect whose short partner Frank Lloyd Wrong insisted on building houses with a six foot ceiling until Cornice became homicidally deranged.
Badger used the phrase in a later episode when feeling homicidal himself.
The Mayor suffers through a brief one when he finds Faith in a coma.
Mayor: She's going to be all right. She'll be all right. She'll be all right.
In "Fear Itself", Oz turns into his werewolf form and runs away from Willow. He is later seen in a bath tub repeatedly telling himself "You're not gonna change..."
Glory's victims tend to speak in these once she fed on their minds.
In Angel the psychotic vampire slayer Dana had several of these, one of which consisted of information on vampire killing she'd never been told.
Chernobyl has poor Aleksandr Akimov insisting repeatedly, "I did everything right" in regards to his actions in the control room of Chernobyl Reactor Number 4 in the early morning hours of April 26, 1986. He was largely not to blame for the reactor exploding, as no one in the control room was aware of a fault in the design of the reactor's control rods, knowledge of which had been suppressed by the Soviet government. Additionally, he was dealing with an unreasonable boss who insisted the test be done improperly, against Akimov's objections. This is apparently true to life, where it's reported that Akimov spent his last days dying of radiation poisoning in a hospital in Moscow repeating these words.
The Collector had a scientist character who sold her soul so she can build a robot. She's able to download her mind into her robot but it won't move. The Devil seals her lab and she is stuck in her robot repeatedly saying "Calculations confirmed. I will move now".
One episode of Criminal Minds had the star played by Frankie Muniz whose Madness Mantra was his now-deceased girlfriend's voicemail message, which included "I'm out living my life. Leave a message!" He was still calling her, because he had once again forgotten she had died. Throughout the episode he was trying to get a hold of her, even though he was with her when she was murdered. The FBI reminding him of that didn't change the fact that he was still suffering a psychotic break. At the end of the episode he's in a padded room with his cell phone just listening to that over and over again, as it was all he had left of her.
In Season 7 when the "Miniature Killer" is finally brought in for questioning, she begins rocking back and forth, reciting the following: "I Have a Pain in My Sawdust."
Nick Stokes's stalker Nigel Crane from the aptly titled episode "Stalker" is reduced to repeating "I am one, who am I? I am one, who am I?" after being caught.
A Season 1 episode of CSI: NY shows Mac laboriously recovering a document from a damaged hard drive that simply says "Three generations are enough" over and over again.
Another case was about a young author murdered by his lover's husband. The man killed him not for having an affair with his wife but for stealing his work. The suspect wrote repeatedly on a notepad "He plagiarized me."
In Dad's Army, when Jones is overcome by terror he starts shouting 'DON'T PANIC!', in increasingly panicked tones.
On Dexter, Angel is hospitalized and has to spend the night next to a patient who was brought over from a mental institution who keeps repeating the words "She knows". He finally snaps and yells that if 'she' knows, then the guy's yapping about it isn't gonna fix anything.
"Doomsday": "I did my duty for Queen and country." Not played completely straight because Yvonne Hartman's Heroic BSoD actually helped her retain some of her personality, and she ended up killing a patrol of fellow Cybermen.
"We shall fly and blaze and slice! We shall fly and blaze and slice!"
Near the end of "Midnight", the Doctor is so rattled by what just happened that he can't do anything but gasp "It's gone. It's gone." for several lines, and is silent for some time after he manages to stop.
In "The Doctor's Wife", the Rory illusion created by House to mess with Amy's head seems to have acquired a madness mantra after spending millennia separated from Amy in the corridors of the TARDIS. Initially, Amy encounters a version of Rory who has aged two thousand years, and he keeps repeating "Every night, they come for me. They hurt me..." Later, Amy discovers a corridor containing Rory's decayed corpse. The walls of the corridor are covered in graffiti in black and red: "Hate Amy, Kill Amy, Die Amy, Hate Amy, Kill Amy, Die Amy..." It's chilling.
Again (only real this time) with Rory in "The Girl Who Waited". While Older!Amy is telling him not to let her in, he can only whisper "I'm so so sorry" over and over again.
"The God Complex": People who find their rooms (and therefore their greatest fears) eventually begin to pray to the monster stalking the halls. Praise him. Praise him. Praise him!
One from the audios: the Eighth Doctor, having spent two and a half episodes on the edge of sanity, falls off it. "Zagreus sits inside your head," BANG! "Zagreus lives among the dead!" BANG! "Zagreus sees you in your bed" BANG! Then later in "Zagreus": "Kill me, kill me, kill me, kill me, kill me..."
Also the audio "Minuet in Hell" starts with the Doctor repeating: "The... legends of Gallifrey speak of a world where everything is horror... horror and pain. A world... from which there is no escape. And the creatures who crawl on the crust of the land are the lost... and the hopeless... and the broken and the doomed. The legends of Gallifrey speak of a world... and the name of the world they speak of is Hell. Hell is where I have come at last... And there can be no escape."
Topher in Dollhouse does this too: "I know what I know."
In The Drew Carey Show, the show regulars read through the day planner of an insane ex-coworker who has started emulating Drew.
"Be more like Drew. Be more like Drew. Be more like Drew. Be Drew."
Stark on Farscape has a tendency to start chanting "My side! Your side! My side! Your side! MY SIDE!YOUR SIDE!" whenever his grip on sanity starts degrading.
Firefly's River Tam may have a very good reason for repeating the phrase "Two by two, hands of blue" when she's upset.
The Mad King died chanting 'burn them all.' The man who killed him said he had been mumbling it for hours. In fact, he apparently continued a couple times more as he was dying.
In Dramatic Irony, the moment something doesn't go his way, Royal Brat Joffrey shrieks a similar "Kill them! KILL THEM ALL!". Tyrion lampshades it's similarity to the Mad King's madness mantra as well, noting how incest has created another Aerys.
Suffering from Cabin Fever and Heroic BSoD in Season 5, Tyrion starts chanting, "I have to get out of this wheelhouse" despite Varys repeatedly pointing out how suicidal it would be for the most wanted man in Westeros to walk about in public.
Varys: (sigh) I'm not sure how many new ways I can find of saying this...
"Hold the door! Hold the door! Holddedor! Hodidor! Hodor! Hodor. As a young man, Wyllis was the victim of being in the presence of Bran greenseeing him while Bran was, in his own present time, warging into Hodor. As a result, young Wyllis got to experience his own death years later, repeating his last directive before that moment over and over again until it devolved from "Hold The Door" into "Hodor".
Will the ranger mutters, "The White Walkers... I saw the White Walkers..." over and over before his execution.
"Reek, Reek, I'm Reek."
Gilligan's Island: In "The Hunter", the ending reveals that the Villain of the Week, who had tried and failed to shoot the young first mate, snapped and was packed off to the mental ward muttering, "Gilligan...Gilligan...Gilligan."
In Hollyoaks, intellectually disabled Spencer Gray was prone to chanting the lyrics of Johnny Cash's "A Boy Named Sue" over and over again during his regular breakdowns. It turned out his foster brother Warren had taught him this as a Survival Mantra ... unfortunately, a lot of the time Warren was the one responsible for pushing Spencer over the edge.
The Kids in the Hall does a pretty good job using this for comedy. "Can't wash the car without a whole lotta milka..."
"Never put salt in your eyes. Never put salt in your eyes. Never never never put salt in your eyes. Your eyes. PUT SALT IN YOUR EYES."
One episode of Law & Order had a psychiatrist whose peace mantra became his then ex-patient, now wife, now killer's Madness Mantra: "I am a rock in a sea of chaos, I am a rock in a sea of chaos..." She murdered him in a rage over his supposed infidelity and pedophilia after listening to his notes for a novel and hearing him wax rhapsodic about "Meredith". The DA reminded her that "Meredith" was in fact the name of the town where they had consummated their relationship, meaning that there was no underage girl with whom he was cheating, only her and that she killed an innocent man.
Lexx: Mantrid: I'VE DESTROYED AN UNIVERSE! I'VE DESTROYED AN UNIVERSE! I'VE DESTROYED AN UNIVERSE!!!
Leonard is a minor character in Lost, a mental patient who keeps chanting the show's Arc Numbers.
Then there's "Theresa falls up the stairs, Theresa falls down the stairs..."
In an early M*A*S*H episode, the storyline revolves around Henry being stalked by a rather unstable, wounded soldier. The soldier desperately wants to return home, worried that his wife had been cheating on him, but was furious at being denied leave on account of the extent of his injuries. Eventually, it gets to the point where a running, unmanned jeep comes crashing through Henry's tent, leaving him so shocked that he repeats over and over "Jeep. Tent. Boom."
Monk, the title character is occasionally prone to this (such as when he was stuck in a powered out elevator).
Particularly in the album version, during Monty Python's sketch of "The Travel Agent", a customer endlessly rambles about his past trips around the world. This gets to be so unbearable that the travel agent just keeps screaming "SHUT UP! SHUT UP! SHUT UP!"
Night Visions featured an episode titled "Now He's Coming Up the Stairs," which starred Luke Perry as a psychiatrist named Dr. Sears with the ability to absorb his patients' mental illnesses, taking them on himself. A worried mother approaches him and explains that she and her young son were in a car accident during which a man crashed through the windshield; the boy went into shock and repeatedly chants "Now he's coming through the woods, now he's coming through the yard, now he's coming in the house, now he's coming up the stairs," thinking that the man is coming to kill him. Dr. Sears heals the boy, and is temporarily plagued with the same nightmarish visions of the man entering the house and attacking the family, but recovers...except that he doesn't actually do so—he overextended himself healing the child and has now gone completely insane. The family's maid finds Dr. Sears in the boy's bedroom, rocking back and forth and endlessly repeating, "Now he's coming through the woods, now he's coming through the yard..."
From the Mad Hatter in Once Upon a Time, who kept saying "Get it to work! Get it to work!" as he's making thousands of hats in Wonderland in a hopeless effort to try to get back home to his daughter and thus revealing how he got his name and how he ended up a permanent character in Wonderland.
When Rumple is discovered to be alive but deranged in season 3, he constantly says "Feed the madness and the madness feeds on you..."
Orphan Black has Helena, who is prone to all sorts of psychopath tropes as it is. After finding out in an intense scuffle that Sarah has assumed the identity of one of the other clones in the series, we get the lovely image of her removing a piece of rebar from her liver, all while repeating what Sarah told her: "I'm not Beth..... I'm not Beth..... I'm not Beth....."
The Outer Limits (1995): In "Afterlife", Stiles chants "They can change my body, but they cannot touch my soul" while being slowly changed by the alien DNA which is spliced with his.
In The Pretender episode "Crazy" Jarod poses as a psychiatric patient and repeats the phrase "Cree craw toad's foot, geese walk barefoot." In a later episode, this is revealed to be a mantra spoken by Edna Raines, a legitimate psychiatric patient. This also qualifies as Arc Words, as Jarod was saying the phrase when he was first brought into the Centre as a little boy in the very first episode.
Shawn from Psych, assigned to hire Da Chief a nanny, rejected a candidate out of hand because she was writing a single phrase in her notes repeatedly. Neither he nor the audience can tell what the phrase was, but Shawn states that "There's no combination of words that makes that acceptable".
Red Dwarf: During one of his fourteen failed attempts to pass the astro-navigation exam necessary to become an officer of the Space Corps, Rimmer suffered a nervous breakdown and ended up writing "I am a fish" 400 times, then did a funny little dance and fainted.
In Rome season 2, Vorenus curses his children for hiding their mother's infidelity from him. Erastes Fulmen catches them and sells them to slavery. Vorenus comes back and he is distraught by their disappearance and he repeatedly says "I shouldn't have cursed them" to himself.
Then there's Servilia's final episode, in which she curses Atia. "Atia of the Julii, I call for justice..."
A scene in Screenwipe has an office worker who keeps typing "I am a flower in a dustbin I am a flower in a dustbin I am a flower in a dustbin I am a flower in a dustbin I am a flower in a dustbin I in a dustbin" on his computer while "In The Air Tonight" plays hauntingly in the background.
In the Smallville episode "Gemini", a hospitalized woman continually mutters in gibberish. Bizarro listens to her and explains that she is speaking in Kryptonian. He translates it, and says she is just saying ones and zeros, and it becomes binary code. When the binary code is translated, it becomes "Error: Reboot" over and over again. Brainiac had jacked the woman's brain.
Happens twice in the Star Trek: The Original Series episode "The Changeling". Once with Spock saying "Sterilize" over and over again after a mind meld gone wrong with the probe NOMAD, the second with NOMAD after Kirk gives it a Logic Bomb, causing the probe to repeatedly shout "Error!".
Twin Peaks: "How's Annie? How's Annie? How's Annie?..." Also, "Oh, mares eat oats and does eat oats and little lambs eat ivy. A kid'll eat ivy too. Wouldn't you?"
The Governor's notebook on The Walking Dead. Apparently when he lost his daughter he went a little nuts and stopped taking careful notes about his settlement and started filling the notebook with page after page of slash marks. Morgan also qualifies after losing his son, gaining an obsession with "clearing", but he gets better with some help.
Wiseguy. "Only the toes, knows." Favourite saying of mad international Arms Dealer Mel Profitt, who shot up drugs between his toes.