Black Mama White Mama: The Defiant Oneswith women! Two female convicts, who are not exactly the best of friends, escape a prison transport while still chained together. It takes most of the movie until they can get the chains off.
Deadlock: This forms the basic plot device in this HBO Original Movie. This film features a futuristic prison with no fences and no guards, the only form of security being explosive collars fitted around the necks of prisoners. Each prisoner has a "wedlock partner," and both partners will have their heads blown off if they place more than 100 yards (approx 100 meters) of distance between them. Since no one knows who their partner is, the prisoners act as their own guards. The story revolves around two prisoners being allowed to escape by revealing to one of them who her partner is, in order that the other partner might lead the warden and his associates to a stash of ill-gotten booty.
District 13: Two prisoners, routine prison transfer, one decides to escape, hate each other, become best friends, one's actually a cop. It's a Subverted Trope in District 13 though – it turns out the prisoner made the other guy as a cop before they even left the police station, but was playing along until the first opportunity to cut himself loose. He then leaves the cop handcuffed to the steering wheel of the police van. It takes a good chunk of screen time for the cop to track him down again, although they then do wind up working together despite their differences.
D.O.A.. In the 1988 remake, the protagonist super-glues his hand to the girl to force her to accompany him. There's one scene where she has to go to the toilet (she ends up going in a darkened alley) and later they get separated when her skin tears free while she's suspended from a lift.
Fled: The movie used this in part, right down to the one black and one white prisoner although Lawrence Fishburne's character is actually an undercover officer.
Jackie Chan: In one movie featuring him, he plays a detective in the early 1900's. At one stage Chan is arrested by his Jerk Ass superior, who handcuffs him to his own wrist in the procedure of the time. Unfortunately, they're attacked by thugs on the way to the police station, and the two have to co-operate to escape and/or fight them.
James Bond and Chinese agent Wai Lin are handcuffed and forced to work together to escape from Corrupt Corporate Executive Elliot Carver's HQ in Tomorrow Never Dies. This isn't just a matter of running and hiding – they end up riding a motorcycle at high speed through crowded streets while the bad guys chase them, still handcuffed together.
The director used Enforced Method Acting there by telling each actor independently that they would be driving the motorcycle, causing quite the scuffle over who actually drives.
The Lone Ranger: John Reid and Tonto spend their first fight against Cavendish shackled together.
Stanley briefly cuffs himself to Lt. Kellaway in his prison escape.
The animated series has Kellaway cuffing himself to Stanley so he'll reveal himself as The Mask. Two villains show up, and Stanley has to find various ways into becoming the hero (KO'ing the cop, bagging his head, standing inside an elevator while Kellaway is outside).
Midnight Run: Through most of the film, the Bounty hunter Jack Walsh (Robert De Niro) is hand-cuffed to Jonathan "The Duke" Mardukas (Charles Grodin).
O Brother, Where Art Thou?: Starts out this way—with three prisoners—but they get unchained fairly early in the movie. They do stick together afterwards, though. (Mostly.)
Revolution (1985): Tom and a big man find themselves tied by the wrists to a heavy effigy of George Washington, made of rope and doused with fox scent. They have to actually drag the effigy while being hunted by hunting dogs and men on horseback.
Rio: This trope holds together not just Blu and Jewel, but also 90% of the plot.
The Silence of the Lambs (Hannibal): A very brief but deadly serious example: Agent Starling handcuffs herself to Lecter to prevent him from escaping (she is too drugged to fight him otherwise). Lecter grabs a nearby butcher knife... and chops off his own hand.
The Specialists: Happens at the beginning of this French movie, in which two prisoners end up chained together during a routine prison transfer and one of them decides to escape. At first they can't stand each other, then they become best friends. Later revealed to be a subversion: the prisoner who decided to escape was actually an undercover cop, chained to the other man on purpose so he'd gain his trust and convince him to work on a robbery. They end up BFF anyway.
Stuck On You: While not a straight example of this trope, this film features conjoined twins; they separate later on in the movie, and neither brother can function nearly as well, as they are used to compensating for the other's weight/movements.
Tonight You're Mine: When a male and a female rock star get into an argument at a music festival, a security guard handcuffs them together for 24 hours.
Who Framed Roger Rabbit: Roger handcuffs himself to Eddie Valiant to get him to help clear his name. Unfortunately, as Eddie angrily tells him, Eddie doesn't have any keys for them, which makes hiding Roger from Judge's Doom's weasels incredibly difficult when they barge in looking for him. When Eddie tries to cut them off, he discovers that Roger can slip off them, but "only when it was funny."
Subverted in The Good The Bad And The Ugly. Tuco is captured by Union forces and transported by train, with a Union soldier handcuffed to him as a guard. Using his bathroom break as a pretense to get near the door, he simply jumps out of the moving train and takes the guard with him. When they land Tuco bashes the man's head in against a rock, then waits with the chain held across the rail for the next train to cut it.