In the manga adaption for Kingdom Hearts, Jasmine winds up bound and gagged after Jafar captures her so she can be taken to Maleficent in Hollow Bastion. In the game, however, she was just unconscious.
First, Megara gets bound and gagged by Pete while she's distracted by Hercules being unconscious. When he tries to lift her dress up, Hades, annoyed with Pete, pushes her into the deepest chambers of the Underworld. Hercules regains consciousness and saves her.
Second, Pluto gets gagged with duct tape while he and Kairi are taken to be imprisoned by Saïx.
Third time. A variant happens to Tron much later on. After saving Sora and his friends, he gets bound to a wall by Sark and is forced to tell the password to the DTD, or face deressolution. He is saved when Sora and co. (unintentionally) crash-land on Sark.
The manga adaptation for Days has two examples, both without gagging involved.
First, during the "Wonderland trilogy", Roxas is sentenced to beheading after the Cheshire Cat pulls a Jackass Genie on him by throwing a hedgehog at the Queen of Hearts. His hands are tied behind his back as he is about to be executed by guillotine. He manages to untie himself just in time.
The second time, the Lost Boys tie up Roxas and Axel when the two are accused of being pirates. Tinker Bell clears their innocence for them.
Peter Pan: Happens to the Lost Boys, John, and Michael when they get ambushed by the pirates. When Wendy walks the plank in the climax, her hands are tied behind her back. Jane also gets gagged in the sequel.
Sleeping Beauty: This is how Maleficent's mooks capture Philip after luring him into the cottage Aurora/Briar Rose had been living in for sixteen years.
In a case of Mood Whiplash, Aladdin is bound and gagged imminently after his and Jasmine's famous carpet ride by Jafar, and tossed off a cliff. He is forced to use his second wish to save himself.
The Hunchback of Notre Dame plays this for Black Comedy in the song, "The Court of Miracles", which has Clopin put Quasimodo and Pheobus, both accused of being Judge Frollo's spies, put on a mock trial, and sentenced to be hanged. The two are unable to defend themselves because they happen to be gagged. Esmeralda clears their names just in time.
At the climax of the film, Esmeralda is tied to a poll to be burned. She is saved by Quasimodo. The scene is also present in Kingdom Hearts 3D: Dream Drop Distance, though not as dramatic, and Quasi himself only says "Sanctuary" once, rather than three times.
In The Little Mermaid II, Melody unintentionally binds and gags Sebastian by tying him behind her with a ribbon when Ariel comes to check up on her. He eventually breaks free, but ruins the party, embarrassing Melody in front of her peers, and gets himself chased by Chef Louis.
At the end of Home on the Range, " Alameda Slim is arrested, and taken away bound-and-gagged in a cart, after his plans were exposed by the cows".
Almost and identical situation happens to Governor Radcliffe in Pocahontas (except in a row boat instead.)
Hilariously done in Ratatouille, with one unusual twist — it's the "good guys" doing the binding and gagging (on a Health Inspector and an interfering former Head Chef)!
Happens to both male and female leads in Tangled, often with Rapunzel's own hair as the bonds. This is very noticeable at the end where Rapunzel is bound and gagged by Gothel after learning that she is the lost princess.
Frozen has Elsa all chained up for a little while. It doesn't last.
Hades binds and gags Meg with smoke to make her seem helpless and so she won't reveal his trap to Hercules.
Done in Treasure Planet when when Jim leaves to retrieve the map from the ship Leaving Captain Amelia and Doctor Doppler all alone with pirates right outside there "safe spot".
In The Avengers, Loki is chained and wears a metal muzzle, most likely to prevent him from using his silver tongue to try and talk his way out, as Thor escorts him back to Asgard to face trial for his crimes on Earth.
In The Lion, the Witch, and the Wardrobe, Edmund is internally chained by the legs inside the White Witch's dungeon. Later on, he is taken by her to be executed on the Stone Table, but after the snow melts, which renders her sleigh useless, she ties him to a tree and gags him. And when Aslan's army saves Edmund, they make Ginabrik take his place.
Jack Black in The Muppets, after getting kidnapped by Miss Piggy, he then spends the entire telethon tied to a chair.
Raiders of the Lost Ark. The Nazis tie Marion Ravenwood to a pole in a tent and gag her. When Indy finds her, he starts untying her, but then realizes that if he does so, the Nazis will start looking for them. This would prevent him from finding the Ark, so he ties her back up and puts her gag back on while she makes loud protests.
This happens to Sora, Donald, and Goofy in Kingdom Hearts II. In Port Royal, the party, along with Jack and Elizabeth, are left tied up after Barbossa captures Will and leaves Gunpowder barrels onboard the Interceptor. Of course, Jack breaks free and unties the others.
Also, during the "Ursula's Revenge" number in Atlantica, Flotsam and Jetsam used their bodies to tightly restrain Sora, which nearly causes him to suffocate (despite being a merman). He gets saved by Donald and Goofy before killing his former captives with a beam of light from his Keyblade.
Earlier in the game, Megara is tied up by Hades. During the boss fight with Pete, she hops around the arena.
And finally, to Santa Claus in Halloween Town, thanks to Oogie Boogie. Santa's yelps even sound like he is gagged, though he really isn't.
Caleb from W.I.T.C.H. gets caught, bound, and gagged in season 1. Lucky for him, he'd done the same thing to the same guards earlier in that episode with his belt, where he kept a dagger that he used to escape.