A similar game mechanic was used in Crash Twinsanity, where Crash and Cortex can latch on to a crystal and Crash can drag Cortex around the level, using him as a mallet and occasionally flinging him across gaps to trigger switches and whatnot.
Divine Divinity's sequel Beyond Divinity uses the trope as its premise – the protagonist becomes forced into Synchronization with a stereotypically villainous Black Knight by a demon, and they work together with the shared goal of not only separating themselves from their rather disliked counterparts, but to get back at the demon who did it to them.
In The Legend of Spyro: Dawn of the Dragon, Spyro spends the entire game chained to former nemesis Cynder. From a gameplay perspective, the main purpose of the chain is to allow co-op play without splitting the screen. However, the chain is also used to solve certain puzzles (for example, one dragon grabs onto a wall and the other dragon swings on the chain to get higher; or one dragon grabs onto a raft while the other dragon flies ahead, pulling the raft forward).
Though the 'chains' in this case are not physical, Bastila treats being forced to go off on a mission that would require spending time with the player character like this in Knights of the Old Republic.
Not so much chained but part of a gameplay mechanic of Knuckles Chaotix revolves around something like this.
In The World Ends with You, Neku becomes spiritually chained to different partners throughout the game. While there is nothing physically forcing them to stay together, the Noise they encounter along the way can only be defeated by two people working together.