In the episode "The Wandering Juvie" we see an entire line of unlikely pairs such as a nun chained to a hooker and Captain McAllister handcuffed to an octopus. They are all waiting for a blacksmith to break them apart.
Used/spoofed in the third-season Family Guy episode "Stuck Together, Torn Apart", in which Stewie and Brian have their hands glued together for a week.
Ron and Barkin get a better understanding of each other, whilst the Bonnie and Kim relationship appears to do the same.. next episode Bonnie is reset back to mega-ultra-superspecial bitch attitude towards Kim.
An episode of Spider-Man: The Animated Series had Spidey and his detractor J. Jonah Jameson both handcuffed to a Time Bomb, which was based on a comic story. Naturally, Jameson just adds it to his list of reasons why Spidey is a menace.
In the TaleSpin episode "Stuck on You", Baloo and his pirate nemesis Don Karnage spend most of the story glued together by industrial adhesive. No Aesop here, they go back to hating each other properly.
Ben 10, episode "Grudge Match", shackles Ben to recurring nemesis Kevin. Unusual in that there doesn't seem to be An Aesop here, unless it's "go with the lesser of two evils." They still hate each other after they separate.
In Duckman, Duckman himself is handcuffed to Agnes Delrooney, the hardened criminal who looks exactly like Grandma-ma by a sinister tobacco baron and the two are forced to make their escape. As Agnes has about 200 lbs on Duckman, it makes for an interesting scene, especially when she gets injured and can't go on.
Adventures of the Galaxy Rangers did an episode forthrightly titled "Chained", with ranger Shane Gooseman and alien outlaw McCross handcuffed together on a frontier planet after their ship crashes (which also makes it an Enemy Mine).
Subverted in that it was only for the first part of the episode, and the two characters only managed to piss each other off worse. McCross's fellow gang members showed up, McCross freed himself, and the rest of the ep is the gang terrorizing Ozark and trying to find a cache of stolen loot. Shane's allies consist of his robot horse and a friendly local.
Happens in the Danny Phantom episode "Life Lessons" when Danny and Valerie are chained together by Skulker as part of his game of hunt when he couldn't decide who was worthy of his skills, so he opted to kill both of them at the same time.
That situation was somewhat subverted, as they only became more friendly with each other in their human forms (Valerie didn't even know that Danny had a Secret Identity, nor did she know that he knew hers), while the next time they met as ghost and ghost hunter, their relationship didn't seem to have changed much.
Rugrats: Angelica and Chuckie accidentally get handcuffed together and lose the key; They eventually find the key and get free, but then Angelica gets handcuffed to her own bed.
An episode of Static Shock has black superhero Static handcuffed to white super thug Hot Streak and the two of them tossed on an island where the Corrupt Corporate Executive is trying to get his son (petrified several seasons ago) brought back to life. They play it straight, wind up as slightly more respectful enemies by the end, and manage to save the kid, although it's more machismo than anything that gets Hot Streak to jump in ("If he can take it, so can I!"). It did show that Hotstreak wasn't all that bad.
Machismo and the fact that he seemed genuinely worried about Static when he couldn't put off enough power to save Edwin.
In Codename: Kids Next Door, Numbuh One and Chad are chained together as part of a subplot of "Op: TREATY". Notably, the usual way this plays out is subverted. It worsens their already tenuous relationship and ends with the two of them fighting to the death in a way that's not played for laughs.
Childrens' show Tweenies once featured all four of the titular toddlers tying themselves together in a row by attempting to help each other with shoelaces, coat toggles, etc. And then Fizz suddenly decided she needed the bathroom.
Transformers Animated did a variant – Bulkhead's wrecking ball got stuck in Mixmaster's cylinder, sticking them together for a chunk of the episode.
Transformers Prime had Bulkhead and Arcee magnetized so that their backs stuck together for most of an episode. Same thing happened with their nemeses, Breakdown and Airachnid.
Transformers Rescue Bots had Buddy Braces, which magnetically tie people or robots together when locked in to enforce the Buddy System on hikes. Kade and Dani were magnetized together, as were the other Burns family members to civilians (or Blades in Cody's case).
In one episode of Liberty's Kids, James gets captured by the British and chained with a Hessian deserter. The two of them manage to escape, and the Hessian takes the opportunity to tell James (and the audience) why the Hessians joined the war.
The Pirates of Dark Water: "The Gameplayers of Undaar." Frog people hijack the ships of both the protagonist Ren and Big Bad Bloth, then force them to complete puzzles while being handcuffed together. Why? "Makes the game more interesting!"
An episode of Doug has the title character handcuffing himself to his Oblivious to Love dream girl Patti Mayonnaise while trying to impress her with a magic trick.
In Storm Hawks, Stork tries to keep the Raptors from getting their hands on a Graviton Crystal by swallowing it, which then causes him and Leugey to be stuck together.
Brandy & Mr. Whiskers spent an episode glued together back to back; on the night when Brandy had a hot date, of course.
An episode of The Batman has Penguin handcuff Batman and Catwoman together. When the two of them stop Penguin and get the key to the cuffs, Batman handcuffs Penguin and Catwoman together for the police to collect.
One episode of Lilo & Stitch: The Series featured an experiment that binds incompatible individuals together with sticky blue goo. Among those who get stuck together are: Lilo and Mertle, Stitch and Nani, Jumba and Pleakley and Gantu and 625.
Variation in the episode of South Park entitled "Super Fun Time". Cartman and Butters are paired up on a field trip and are told not to let go of the other's hand until they get back on the bus. Despite the many MANY hijinks that the pair get into (which include dangling on either side of a traffic light), Butters will not let go of Cartman's hand because Mr. Garrison said not to. It's like handcuffs, only without the handcuffs.
Butters:(at the very end of the episode, after dragging Cartman's unconscious body past everyone) Teacher...MY PARTNER IS BACK ON THE BUS.
Looney Tunes, "D'Fightin' Ones" Sylvester the cat and a bulldog are chained together and on the run from the dog catcher in a direct parody of the previously-mentioned The Defiant Ones. They do manage to break the chain at the end, they then get their legs jammed together in a pipe and go hopping off in frustration.
Darkwing Duck spends an episode attached to his bumbling neighbor Herb Mudlefoot when contact with an electric fence causes their wristbands to weld together.
Happened in the Jackie Chan Adventures episode "The Chan Who Knows Too Much" between Jackie and Jade thanks to a corrupt cop.
An episode of Jimmy Two-Shoes has Heloise fusing Beezy and Jimmy together in hopes that they will get sick of each other. The episode ends with Heloise stuck to them as well, who enjoys being so close to Jimmy.
Word of God says that there was going to be an episode of Avatar: The Last Airbender where Sokka and Aang were handcuffed to each other. The decided not to because they had to make more important episodes.
The Flintstones did an episode where Fred and Barney become stuck to a bowling ball together.
There was an episode of Dexter's Laboratory where Dee Dee and Dexter got stuck together with a seemingly invincible Chinese finger trap.
In one episode of Aladdin: The Series, a villain causes Aladdin and Rasoul to be magically bound when he sees how much they dislike working with each other. The chain's length varies on how argumentative they're being. If they're fighting, the manacles fuse together, if they agree to put up with each other there's a decent length to work with, and when they're genuinely getting along they're unchained until they fight again.
Pelswick had an episode that features the bully chained to the protagonist's wheelchair, in a Whole Plot Reference to The Defiant Ones. Pelswick himself was even told to watch the film by his guardian angel, but refuses on the grounds that it's a black and white film, though he does get one of his friends to watch it and tell him about it.