In one chapter of Ah! My Goddess, Keichii and Belldandy end up with their hands magically glued to each other for a day because of a spell Belldandy accidentally cast while drunk on cola. It's mostly played for the physical and social awkwardness, as their relationship spends forty-odd volumes on a very slow burn, and now they can't stop holding hands.
There are no literal chains in Double Arts—just the simple awareness that if Kiri lets go of her hand for more than a few seconds, Ellie will go into a horrific seizure and die. Needless to say, they are, for all practical purposes, just as good as chained together.
Although they were able to take advantage of it not being exactly the same in the first chapter to win a fight by switching hands to get an advantage.
In the Gintama anime, Hijikata and Okita are chained together at the neck with exploding collars as a parody of the Saw franchise. They spend the next few days foiling each other's attempts at escape.
Hijikata got handcuffed to Gintoki and had to request his help in taking down some bad guys. Hilarity Ensues.
In Seo Kouji's oneshot manga Half & Half, the male and female protagonists are both involved in an accident and die together. Then a rather generic Kami-Sama gives them a chance to live again, for 7 more days; the catch is that after the time limit, one of them must die again. They're forced to stay together until they decide, else they both die.
In a side story of Kamichama Karin, Karin and Kazune'smagic rings ends up stuck together, and by extension their hands. Instead of having to make excuses for cuffs, they have to avoid being seen with their hands stuck together or face the wrath of Kazune's Fangirls. This leads to some rather funny moments where Kazune has to go to the bathroom and where they have to change for gym. The latter leads to a Funny Moment where their enemy walks in on them in a... compromising position.
Has happened a couple of times in Lupin III, when Zenigata actually manages to cuff Lupin. And quickly learns that the downside to cuffing yourself to Lupin, is that you are now cuffed to Lupin. And he isn't chained to anyone.
A Naruto filler episode recounts an instance where the original Team Kakashi faced a gang of thieves lead by Ninja Spiderman(the guy even webswings in one scene). Naruto and Sasuke wind up with their hands webbed together for the remainder of the flashback. During the Hilarity Ensues scene of trying to seperate themselves, they accidentally kiss... again.
Also in the Pokémon Adventures manga with Green's Ditto and Sabrina during a battle. Hilariously, Sabrina was furious to find out that they weren't even chained together at all.
Pokémon: Volcanion and the Mechanical Marvel: Most of the movie has Ash tied with a futuristic magnetic band to the eponymous Volcanion, a large Fire/Water tank-like Pokémon that has a deep mistrust of humans. Obviously, Volcanion is not thrilled at the prospects of being tied with one.
In the manga as well as an episode of Princess Resurrection. Riza, a half-werewolf, handcuffs herself to Reiri, a vampire, in order to insure that the latter would take her on a rescue mission. Unfortunately(Or fortunately) for the duo, Riza didn't have the keys, so they need to go through the mission chained together in order to take them off.
Having two characters chained together actually happens fairly often in Ranma ½. Somewhat subverted in that they very seldom get along and generally find some way of using the other as the weighted end of a chained weapon.
Such as Ranma using P-chan as both a shield and blunt object in a Martial Arts Gymnastics match with Kodachi.
"Pig is a valid weapon."
Invoked in the story where Gosunkugi orders a set of Powered Armor to defeat Ranma. It does make him powerful, with a few caveats: he needs to be tethered to someone he hates just to move around in it, and he absolutely needs to land a punch on that person, or the armor will explode with him in it. Unfortunately for him, Ranma isn't willing to make it easy, self-preservation be damned.
Sailor Moon: An attack by a Daimon handcuffs Sailor Moon and Sailor Uranus together for an episode. This serves as a plot device since they'd been at odds since they ran into each other and have avoided contact. Being stuck together helps each to understand how the other thinks.
In the manga Train Plus Train, average everynerd Reiichi Sakasuka ends up handcuffed to fugitive Arena Pendleton. The cuffs are indestructible, but time-released. They just had to wait 99 hours, which meant that Reiichi had to cancel all his plans and go on the run with her. This was just the beginning of the tension between them.
In Detective Conan, when Heiji Hattori and Kazuha Touyama were kids, they got handcuffed while playing with a pair that belonged to Heiji's policeman dad. They spent a whole a day like that, and when they were released, Heiji kept an amulet made with a piece of said 'cuffs. Which would later become a Pocket Protector, and save Conan from being stabbed to death.
Downplayed in Gunslinger Girl. Mimi Machiavelli, daughter of a witness who's testifying in a mob trial, handcuffs Hilshire and Triela together and nicks out the door to see her boyfriend. However rather than chasing her, Hilshire just calls the other operatives to pick her up. Hilshire and Triela's relationship is rather tense at the time, but this scene follows:
Hilshire: Say, what did she mean by we should "Talk about love"? Triela:(picking the lock on their handcuffs) I think she's got the wrong idea about us. Hilshire: We're fratello. We don't need to talk about love.