Eren Yeager, the protagonist of Attack on Titan, is subjected to this on multiple occasions. As the Living MacGuffin, multiple arcs have focused on him being arrested or kidnapped by various parties. This also prevents him from biting into his hand, the trigger for his titan transformations.
This happens to Orihime twice in Bleach, although the first is only implied- Ulquiorra tells Orihime (who is upset because she believes one of her friends is dead) to eat. She refuses, so Ulquiorra tells her if she doesn't eat then he will strap her down and force it down her throat. We never see Orihime eat after that, so it's hard to tell if he followed up on this. Second time was with Grimmjow after he stole her out of her room to go heal Ichigo so Grimmjow could fight him properly.
Code Geass has this increasingly through out the series. Nunally twice, Vileta once, Cornelia once and others. Kallen and Lelouch are, when captured, forced to wear strait jackets; CC has one as her ''daily clothing'. Also carried out by the soldiers involved in the Chinese uprising. Why were they carrying ballgags with them again?
Cross Ange featured many of these types of scenes in every other episode.
FLCL. In episode 1 a hospital nurse ends up this way after she's Mugged for Disguise by Haruko to get her uniform.
Gensomaden Saiyuki. During a filler episode, the Anti-VillainMs. Fanservice Yaone was captured by a group of demon-hunting humans and was tied to an X-shaped cross. There was no gag, but the anime utilized a lot of dark lighting and only a few glimpses of her bound wrists and sometimes her body, treating her situation as a really dead serious distress. Because the group is led by a demon who just wanted to consume other demons to attain more power for himself, and if it wasn't for both Kougaiji and Sanzo's groups rescuing her, she would've been the next one consumed.
In Guardian Fairy Michel, Michel and Kim end up trapped in a net, then tied up and gagged in episode 3 to prevent them from telling the truth about Salome and her gang to a prospective mark.
Hanaukyō Maid Team La Verite episode 6. In the Baseball Episode, the maid acting as an umpire is kidnapped (and shown tied up and gagged) and replaced with a Technology Department robot.
Mazinger Z: In episode 27, Sayaka was captured by Baron Ashura, and she got tied to a supporting beam to prevent her from escaping. Partially remade in the remake Mazinkaiser.
Happens quite often in Mnemosyne, Episode 1, Rin is strapped down and tortured by Sayara. Episode 3, Rin is bound to the handrails of sinking ship. Episode 6, Rin is chained to a table and ball-gagged in front of a chained Angel by Laura. Then there is Apos' torture victim in various episodes.
Happens to Allelujah Haptism in Mobile Suit Gundam 00. After the final battle of Operation Fallen Angels, he was captured by the UN Forces and was imprisoned like this (restrained to a metal chair and was put in a straitjacket with a muzzle covering his mouth) for four years. He was finally rescued by Celestial Being in Season 2 Episode 3.
Tenma is captured, tied to a chair, and beaten by a dwarf Neo-Nazi crime lord in Monster. The scene is doubly valuable as a great demonstration of Heroic Spirit and Fanservice.
Naruto gets tied up and gagged in one of the movies. As does Sasuke way back in Part 1, by Naruto, although he easily escapes.
Ōkami-san: Ōkami gets tied up by some school bullies in episode 2.
In "The Punchy Pokémon", Team Rocket leave a trainer tied up and gagged in a bathroom stall and steal his Hitmonlee, as well as his clothes, in order to compete in a Fighting-type Pokémon tournament.
In "Just Add Water", Misty ends up tied up with Dorian, both with tape across their mouths, after accidentally being captured alongside some Water-type Pokémon by Team Rocket.
May couldn't catch a break with this in Pokémon the Series: Ruby and Sapphire, with many episodes having her as the Designated Victim, either tied up by Team Rocket (eg. "Who, What, When, Where, Wynaut?") or attacked with String Shot by a bug Pokémon (eg. "Caterpie's Big Dilemma"). Some were group scenarios, but May was almost always involved.
Marina of The Legend of Thunder gets bound and gagged while captured by Team Rocket duo Attila and Hun. She is saved by Jimmy's Beedrill.
In "Turning the Other Mask!", Molayne gets tied up and gagged by James and Faba after they mistake him for an impostor trying to steal the Masked Royal's identity.
At one point in the Ruby/Sapphire arc, Flannery gets kidnapped by Team Aqua. She ends up with her hands tied to her back and with tape across her mouth. Same with Tucker in the Emerald arc.
Later on, during the Black/White arc, an undercover Grimsley ties up a Team Plasma grunt pretending to be a construction worker after knocking him out. He leaves the grunt behind to be punished, along with a comatose Black.
In Pokémon Origins, Mr. Fuji is bound at the wrists and ankles while taken hostage by Team Rocket.
Akane from Ranma ½ found herself in this predicament when Cologne tied her up and hid her in a storeroom, to keep her from interfering with Shampoo's plots. Surprisingly, even when Akane is more than capable of breaking free on her own, she refused to do so because Ranma was being a great big Jerkass. This is a persistently common trope in the series. Another incident involved Pantyhose Taro holding her as a hostage, and keeping her gagged and bound with (you guessed it) pantyhose.
In SPY×FAMILY, Anya Forger is kidnapped by thugs working for a corrupt government official when she accidentally transmits a message to them using Loid's spy gear. When next we see her, she's sitting in a shopping cart with her arms tied and a piece of tape over her mouth.
No gagging involved, but in Strawberry Marshmallow, Miu called Nobue to tell her that Matsuri was her prisoner and was being tied up with a long rope. She demanded 5000 yen (a little less than US$50) or she would remove Matsuri's panties. Nobue went over to find... Miu tied up. Nobue took Miu's wallet, removed a 5000 yen note, and left over Miu's protests.
Time Stop Hero: Kuzuno Sekai can stop time and often uses this to neutralize opponents without much of a fight. Since he refuses to harm women, his usual tactic is to stop time, then strip them naked, tie them up, and/or gag them. From their perspective, it is as if he can strip and/or bind them in an instant. The gag can neutralize magic users who have to chant their spells.
Yakitori: Soldiers of Misfortune. In the Season One finale, Unit K-321 are handcuffed and mouth-masked during their own court-martial. Fortunately it's not the Kangaroo Court it was intended to be, as their attorney proves more than capable of speaking on their behalf. Given the way the hot-tempered Akira keeps trying to interject or punch people, it's probably just as well.
In YuYu Hakusho, Kuwabara is tied and gagged in the Chapter Black arc in order for Sensui to use his Jigen-tou to slice through the dimensions- first with Toguro-ani's body working through Gourmet, then with a conventional rope and gag.
In Yo Kai Watch, Indy Jaws is tied up with rope and gagged with his own bandana by local yokai in the jungle along with Jibanyan (although the latter isn't gagged).
