The A-Team, "Breakout": BA and Murdock got caught by a small town sheriff and put on the local chain gang. While inside, there's a prison break and the escaping prisoners handcuffed them together while they tended to a guard who got shot. Murdock brings up the Defiant Ones.
Brooklyn Nine-Nine: In "Christmas", Peralta handcuffs himself to Holt and throws the key down a grate to keep him from leaving the safe house. Holt calls Boyle to fetch him, but when Boyle can't decide whether to remove the cuffs or not, he panics and cuffs himself to Holt as well.
Castle: Has Beckett and Castle waking up handcuffed together in the appropriately named episode "Cuffed". This trope is lampshaded by Esposito and Ryan when discussing how a relationship can have a make-or-break moment when two people are stuck together in close proximity.
Charlie's Angels: In the episode "Angels in Chains", Jill, Kelly, and Sabrina are chained together when they try to escape from the prison warden.
On Designing Women, Charlene, her fiancee and a stripper from his bachelor party wind up locked together in a set of menage-a-trios handcuffs.
Eureka: Action Girl Jo and town Jerk Ass Zane are accidentally locked together at the ankle by a quick acting cement-like substance. Right after they had broken up.
Even Stevens: The school guidance counselor attempted to enforce this trope on Ren and her rival Larry Beale together. They end up pretending to get along just to get her to unlink them, but as they have to work together to pull this off, in the end they're worried that it might have actually worked.
The Facts of Life: Blair and Jo end up handcuffed together as a result of a dispute over a story Jo wanted to run on the Langley College newscast. The Credits Gag at the end sees an unidentified staffer try to saw the chain off.
Family Matters: Did a surprisingly decent (for them) version of the trope, where Lieutenant Murtagh and Carl are on a stakeout. Murtagh, incompetent as always, is playing with trick cuffs...only to find that once he has them on the two of them he can't remember the spot that will release them.
Frasier: Handcuffs himself to a stripper in a police officer costume. She doesn't have the key because the cuffs were intended for use as a prop only.
F Troop: In "The Day They Shot Agarn", Parmenter and Agarn end up handcuffed to each wrist of a prisoner. Later the prisoner escapes, still handcuffed to Agarn.
Green Acres: One episode had Oliver show Lisa how handcuffs work, only to find he had lost the keys.
Hannah Montana: In one episode, Oliver handcuffs Miley and Lily together while they are fighting and then discovers he doesn't have the key. Happens a second time with Lily and Oliver being glued to each other via chairs.
I Love Lucy: One episode did this when Lucy handcuffs Ricky as a joke. But finds out she grabbed the wrong handcuffs (She thought they were Fred's trick ones) and the two end up having to go through the whole episode with them on.
Inspector Morse: Something similar was the reason behind a murder in this show. Two security guards had conspired to rob a payroll in a suitcase attached by a chain to the wrist, only one had left the key behind when he changed his jacket.
James May's Man Lab invokes the trope for the orienteering segment; James and Oz are handcuffed to each other as they escape Dartmoor Prison.
Kamen Rider Double (Kamen Rider Accel): In the direct-to-video movie, protagonist Ryuu (a policeman) spends about half the movie handcuffed to an attractive pickpocket, which produces even more Not What It Looks Like than he's already in and almost causes his wife to divorce him.
Kate And Allie had an episode where the two got in a fight. To get them to work it out, the kids handcuffed them together in the kitchen through a counter, then left them.
Leverage: Features this with Hardison and Eliot as they are fleeing from a militia group in "The Gone Fishin' Job". They eventually get out of their restraints, but are first able to defeat several members of the group and improvise a bomb with a cigarette.
Lost: Subverted Trope, with Kate and Juliet waking up in the jungle handcuffed together, Juliet claiming that she was knocked out by the rest of the Others and left behind. While at first it seems that they are starting to get along, it turns out that Juliet dragged Kate out into the jungle and handcuffed them together in order to gain her trust. Her deception is unmasked when the two are menaced by the Smoke Monster, and Juliet unlocks the handcuffs in panic so that she can turn on the security barrier.
Upping the drama factor, the guest character was played by Alan Alda's real-life father.
By the way, Alan Alda's stepbrother also had a minor role in the episode.
Mission: Impossible: In the episode "Nerves", the IMF stage one of these. Casey poses as a prisoner and is handcuffed to the villain's girlfriend. The IMF stage a breakout so that the girlfriend takes Casey to the villains hideout. Before that, in a first-season episode the IMF stages a prison break for a potential assassin while handcuffed to Rollin.
NCIS ("Chained"): An undercover DiNozzo is handcuffed to a convict; they escape together and go find a stash of stolen Iraqi antiques that NCIS is searching for.
Ned's Declassified School Survival Guide does this in one episode. The school spirit stick can't touch the ground, and two characters are trying to pass it off on each other in increasingly ridiculous ways, until one tries superglue and they end up stuck together for the remainder of the episode.
Power Rangers Samurai: Kevin and Mike wind up with an extra-difficult version of this; both their hands are stuck together by a Nighlok with a glue attack.
Prison Break: Had an interesting take on this setup when they finally got out of the prison (Season 2). T-Bag, who wasn't on the escape plans and forced himself in was afraid, with reason, that they would try to get rid of him as soon as he could no longer tell the guards of the plan. So, he handcuffs himself to Michael, and now they have to take him along, because they cannot be separated and Michael is just too important to Abruzzi (the guy with the escape jet). Then they reach a kind of barn, where Abruzzi picks up a saw and tries to cut the handcuffs, to no avail. Then he chops off T-Bag's arm.
Psychoville: Mr Jelly performs at a retirement home and accidentally handcuffs himself to one of the elderly residents, leaving them stuck together while on the run from Mr Jolly's killer – or so they think.
Quantum Leap: One episode followed the premise (or the whole plot ?) of The Defiant Ones, with Sam escaping a prison while handcuffed with a black man....
The Rat Patrol: In the "Chain of Death Raid" episode, American Sgt. Troy and German Captain Dietrich were captured by Arabs and chained together, forcing them to cooperate in order to escape. [Just one of several Enemy Mine episodes in this series!]
Revolution: The title of the episode "Chained Heat" matches the trope name. The episode features slaves being chained together and forced to drag helicopters for the Monroe Republic. The protagonists end up freeing the slaves.
Round the Twist: Faye handcuffs herself to Mr Gribble, shortly before going into labour, in the last episode.
Spartacus: Blood and Sand had an episode where two-man teams of gladiators were chained together and put into a battle royale match. Naturally, the team of Spartacus and Varro were the last men standing.
Stargate SG-1: Vala pulls this on Daniel with a pair of linked Goa'uld bracelets that cause the wearers to fall into a coma if separated for too long, though her motive was to ensure that she didn't get left out of a share of the treasure at the end of SG1's current quest.
Star Trek: The Next Generation: The episode "Attached" had an interesting variation on this trope. Picard and Crusher, who each had feelings for the other, wound up together on a hostile alien planet. They weren't physically chained together, but were fitted with devices that allowed them read each other's thoughts, but also prevented them from moving more than ten feet apart without feeling extreme pain. Hijinks ensue. To be clear, said devices were intended to eventually sync fully to their brain chemistry, at which point their captors would simply download their memories. The telepathy was a side effect.
The Suite Life of Zack and Cody (The Suite Life On Deck): Mr. Blanket, the school's insane Guidance Counselor, handcuffs Moseby and Zack together, and swallows the key. It helps them understand one another better, but also increases their contempt for Blanket.
Supernatural: Had this happen to Sam and Dean when they were arrested. It was both played straight (they work together to prove their innocence) and Played for Laughs (trying to sit down on opposite ends of a bench, the brothers trip and almost fall flat on their ass.)
Tales from the Crypt: One episode has a variation in which an escaped convict is handcuffed to the cop who is chasing him, then shoots the cop – who manages to swallow the cuff key before dying. The convict then spends the rest of the episode dragging a dead cop around by the wrist.
Three's Company: Jack handcuffs himself to Chrissy, not realizing she doesn't have the keys. Since he has a hot date, he decides to make Chrissy tag along (sitting at the next table). Hilarity Ensues.
Wizards and Warriors: One episode has good prince Eric Greystone and evil prince Dirk Blackpool trying to escape a dungeon of deathtraps while chained together.
The X-Files: In "Piper Maru" Agent Mulder handcuffs himself to a female secrets broker, so as to force her to take him to her contact. It turns out to be Krycek, who shoves the woman through a door and slams it shut on the chain, trapping Mulder. Moments later the woman is shot dead by French Secret Service mooks, and Krycek flees leaving Mulder to his fate. Fortunately he's able to find the handcuff key before they kick down the door.
Quark. In "All the Emperor's Quasi Norms", Blood Knight Gene is chained to cowardly Tin-Can Robot Andy while escaping a Gorgon ship. At one point Gene tries to leap off a railing to attack some guards beneath, only to be left dangling when Andy refuses to follow.