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?
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.
In Yu Yu 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.
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.
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.
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.
Hanaukyō Maid Tai 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.
Ōkami-san: Okami gets tied up by some school bullies in episode 2.
Happens to a few characters in Love Hina, thanks in part to Kanako being adept at this sort of thing.
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 quite a few times in the Pokémon anime, this.
In the episode "Just Add Water", Misty is tied up with Dorian with tape across her mouth.
May couldn't catch a break with this in the Advanced Generation series. Many episodes she was the Designated Victim ended up with her being tied up by Team Rocket (eg. "Who, What, When, Where, Wynaut?") or attacked with String Shot by a bug Pokemon (eg. "Caterpie's Big Dilemma"). Some were group scenarios, but May was almost always involved.
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.
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.
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.
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.
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.
Fujiko Mine from Lupin III has been a victim of this in most of her incarnations across the decades.
Cross Ange featured many of these types of scenes in every other episode.
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.
Happens regularly in Detective Conan. Perhaps unsurprising, it being a detective show.
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.