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.
In Kingdom Hearts II, Pluto is gagged with duct tape while he and Kairi are taken to be imprisoned by Saïx.
Also, when Hercules is unconscious, Pete bounds and gags Megara while she's distracted. When he tries to lift her dress up, Hades, annoyed with Pete, pushes her into the deepest chambers of the Underworld. Of course, she is saved by Hercules.
Though it might not really count as being tied up, Tron is bound to a wall by Sark and is forced into a negotiation. His anti-MCP comments get him tortured a few times.
Peter Pan: Happens to the Lost Boys, John, and Michael when captured by the pirates. It also happens to Wendy's daughter, Jane, 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.
Happens to Aladdin, following A Whole New World. He is forced to use his second wish to save himself.
The Hunchback of Notre Dame: Happens to Quasimodo and Phoebus when they reach the Court of Miracles to warn Esmeralda that Frollo has found its location. They are accused of being Frollo's spies and sentenced to be hanged in a mock trial during a musical number, but Esmeralda manages to clear their names 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. She survives in the film, but dies in the German Broadway version.
In The Little Mermaid II, Ariel unintentionally binds and gags Sebastian by tying him to Melody with a ribbon. He breaks free, but ruins the party, embarrassing Melody in front of her date, 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.
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.
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.