24: This will frequently happen to characters like Damsel Scrappy. Kim Bauer, daughter of Jack Bauer, was captured, bound, and gagged by the bad guys no less than three times over the course of the series (including by one Faux Mole). And once more in the video game, to boot.
Agatha Raisin: In "Agatha and the Wizard of Evesham", the killer uses duct tape to gag Agatha and bind her to her to a hairdressing chair.
The Avengers (1960s): Emma Peel. Routinely. The only times she ever seems remotely put out by this is when it looks like a related Death Trap might go off while she's still, ah, indisposed.
Batman (1966): This happened quite a lot to several characters throughout the course of this show. The Dynamic Duo were often tied up during the cliffhangers, although they were gagged only a few times. And after being introduced at the beginning of the third season, Batgirl was tied up (while sometimes being gagged) quite a few times as well.
Castle: One episode sees the main character being bound and gagged by his daughter to see how he can escape for a book idea. Said daughter takes the chance to empty his wallet to go shopping.
Criminal Minds features many UnSubs who do this to their victims. On the main character side, we have Morgan ("Our Darkest Hour"/"The Longest Night"), Reid (three times), Hotch ("LDSK"), Prentiss ("Minimal Loss"/"Lauren") and Blake ("The Replicator").
CSI: Subverted in one episode where there was an apparent robbery of priceless antiques with the guard bound with a long length of duct tape. However Gil Grissom's first clue that the robbery was as a fake was when he discovered that by the position of the tied up guard and nearby fixtures, the evidence strongly suggested that the guard tied himself up.
Elementary did this most notably in "A Giant Gun, Filled With Drugs" to the daughter of one of Sherlock's old friends.
Endeavour: In "Degüello", the crooks kidnap Max in order to lure Morse into an ambush. When Morse arrives at the quarry, Max is bound and gagged and lying in the back of a builder's truck.
The F.B.I.: In "To Free My Enemy", a pornographer is kidnapped and his kidnappers keep him bound and gagged on the bed in the abandoned hotel they are using as a hideout.
Firefly: It didn't feature a whole lot of gagging, it did feature a lot of binding, particularly toward the show's resident Damsels In Distress, River and Kaylee. As a point of irony, by the time of the Big Damn Movie, River's newfound lethality allowed her to slip out of most of the binding she would have faced earlier in the series.
The Fresh Prince of Bel-Air: Played for Laughs. During a montage in which Will and Carlton are renovating an old apartment, Will gets fed up with Carlton bossing him around so he sticks him to a wall and gags him with an apple he was eating for good measure.
Fringe: In the episode, "August" (which reveals the existence of more than one Observer), an Observer kidnaps Christine Hollis and has her bound and gagged for most of the episode at a motel.
After Jaime's failed escape, Catelyn orders, "Take him back to his cell. Bind him with every chain you can find," then adds "...and gag him!" when he continues to snark at her.
Tyrion is treated to this after his capture in "The High Sparrow". Tyrion grunts constantly at his captor until he gets annoyed and removes the gag.
Cersei has Ellaria and Tyene Sand chained to the wall and gagged so they can't spit, curse, or beg while she taunts them about their upcoming Fate Worse than Death.
Gosei Sentai Dairanger: Early in the episode, Zhangliao captures Daigo, Kazu and Lin and ties them on three poles and gives each of them a gag.
Jonathan Creek: In "The Sinner and the Sandman", Jonathan finds two people bound, gagged and tied to chairs, and unties them. Unfortunately for him, they are a pair of burglars the real householders had overpowered and tied up to await the police.
Quarles likes to bind and torture male hustlers. In "The Man Behind the Curtain," Sammy Tonin mentions the rentboy back in Detroit whom Quarles left in a coma, an incident that played a role in Quarles' exile to Kentucky. Several episodes show Brady gagged, nearly naked, and bound to a bed in Quarles house before Quarles presumably kills him. At the end of "Guy Walks into a Bar," Donovan is shown bound and gagged in a bathroom as a naked Quarles approaches.
In "For Blood or Money", Clinton leaves both the manager of his halfway house and his mother-in-law bound and gagged in the string of crimes he commits while attempting to get to his son's 12th birthday.
Law & Order: Criminal Intent: In "Please Note We Are No Longer Accepting Letters of Recommendation from Henry Kissinger", a distraught woman takes over a preschool. She ties the director and a teacher to chairs and gags them. They are in the room as Goren attempts to talk her down.
Lost: The season 2 finale saw Jack, Kate, Sawyer, and Hurley bound and gagged by the Others, though the gags were largely unnecessary.
The Magician: After knocking Dennis out, a hitman leaves him bound and gagged in his wheelchair as he prepares to assassinate Max in "The Manhunters".
In "Left for Dead", the murderer leaves Tom Barnaby bound and gagged on a mattress in the cellar. He has to be rescued by Jones.
In "The Dark Rider", the killer attempts to remove someone who is afraid of the dark from the line of succession by driving them into a permanent state of trauma by leaving them bound and gagged inside a priest hole.
In "Sting of Death", the killer places their third victim inside a sarcophagus which they start to fill with honey.
Miss Fisher's Murder Mysteries: Dot, Aunt Prudence and Mr Butler are gagged and tied to chairs by a killer who is waiting in ambush for Phryne in "Death at the Grand".
Murder, She Wrote: In "The Murder Channel", a friend of Jessica's accidentally stumbles on a plot of some thieves. The thieves kidnap and keep her bound and gagged in the back of their van as they commit the robbery.
Murdoch Mysteries: In "Convalescence", Mrs Kitchen is kept bound and gagged while the criminals search her house for the missing loot.
NCIS: At one point or another, Jenny, Ziva, Paula Cassidy, EJ and Palmer all end up this way, not always with the gagging. It should be noted that while those are mostly female names on the list, the show does not have a fetish-based or Distressed Damsel bent. It seems to be mostly coincidence.
In Season One, Episode 17 "Hat Trick," Emma Swan was drugged by Jefferson (aka The Mad Hatter) and woke up bound and gagged in his living room. Fortunately for her, she managed to break a nearby teacup and cut her bonds. She then discovered Mary Margret Blanchard (aka Snow White) bound and gagged in another room in Jefferson's house. She attempted to free her but unfortunate Jefferson forced her to tie her friend back up in order to meet his demands of making his magical hat work again. Later in the episode, Emma manages to free Mary Margret.
In Season 2, at the end of Episode 19 "Lacey" and the beginning of Episode 20 "The Evil Queen," Tamara reveals to Greg Mendell that she brought a "package" back from New York, opening the back of a trailer to reveal Captain Hook bound with white rope and gagged inside.
In Season 5 Episode 7 "Nimue," Mary Margret is unfortunate bound and gagged again, this time by Zelena the Wicked Witch of the West after being tricked by the pregnant woman with fake contractions. The witch used Mary Margret as a hostage in order to get the rest of the group to not attack her and carry out her plan with King Arthur.
Rebelde Way: Marizza is victim to this once Pablo kidnaps her and holds her imprisoned in his apartment. Also happened frequently in season 1 to the boys whenever the Logia appeared and captured them for interrogation (at least it happened to Manuel, Pablo, Nico and Marcos).
Revolution: In Episode 4, Charlie Matheson gets captured by Ray Kinsey, and ends up bound and gagged.
Round the Twist: In "The Whirling Derfish", Pete overhears Gribs and his lackeys discussing a plan to make Bronson, who had swallowed a magical fish that gave him the ability to swim incredibly fast, lose a swimming competition. When he confronts them about it, they promptly bind him in red tape and gag him, also keeping him from participating in said competition.
Scorpion: Happens to Cabe's ex-wife Rebecca when she is kidnapped in "Rogue Element".
A Series of Unfortunate Events (2017): In "The Bad Beginning", Count Olaf captures Sunny Baudelaire, he ties her up with rope, puts tape over her mouth, and dangles her out of a tower window in a birdcage. This seriously impedes Sunny's ability to speak, even though most people cannot understand her to begin with, but her words are still translated for the audience. However, she doesn't stay like this for very long as the Netflix series added a humorous scene in which Sunny Baudelaire and Fernald (aka the Hook-Handed Man) play poker. Despite her bonds, Sunny is still able to deal cards and she ends up winning multiple hands to which the Hook-Handed Man ends up being tied up and have tape over his mouth due to him losing the game.
Sherlock: In the second episode, John and Sarah are kidnapped by Chinese gangsters and tied up, though only Sarah is gagged. Later in the second series, a CIA agent is bound and gagged with duct tape by Sherlock after he attacks Sherlock's landlady.
She Spies: Uses ropes and gags for its frequently-captured main characters. The show's mood is so light-hearted as to be downright corny.
Snobs: Female protagonist Abby Oakley ends up like this in episode 5 of this Australian series after she gets caught snooping by a pair of computer thieves who have managed to get her friend and fellow protagonist Marianframed for one of their thefts. She is held captive below deck on their boat, where she is tied to a chair and has her mouth taped shut, with the thieves planning to drop her off unharmed at a relatively out of the way location so that she'll have no choice but to take the long way home afterward...by which point the thieves plan to already be long gone with the money they'll have hopefully obtained from selling the stolen computers. Thanks to Marian and their titular canine companion Snobs, she is able to successfully get free and escape.
In the episode "Hunted", you would be forgiven for thinking that Dean like this was the main attraction, considering as most of the pictures released/trailers shown have him tied up. Guess they know who their audience is.
And when Castiel had duct-tape over his mouth in "Changing Channels", livejournal icons of the scene popped up almost instantly.
Supernatural also has its fair share of girls tied up, either needing to be rescued by the heroes, or having been tied up by the heroes because they are monsters or possessed by demons.
Teen Wolf: The hunters seem to like this method a lot, seeing as how Chris had himself and Allison bound up and gagged as a training exercise and Gerard did this to Erica and Boyd once they'd been captured.
Sarah spends almost an entire episode like this in the back of a guy's van. One wonders why he bothered with the gag at all, since every time she woke up with it on she just pulled it off.
Also, earlier in the series, Charlie's wife is kidnapped by Cromartie and bound and gagged in an old abandoned house.
Sarah's tied up by Cromartie in the episode Mr. Ferguson is Ill Today. And in the first season, Dr. Silberman ties James Ellison up and sets the house on fire to kill him.
Tom Turbo: An example of fantastical fare from Germany. This is a series about a talking bicycle and the random kids who help it solve mysteries, has someone tied up in more than half the episodes. That someone could be anyone from an adult who needs rescuing to one of the main child characters. Or both at the same time.
Top Gear: Clarkson is bound and gagged to a tree so May can make fun of... er, review the Ford GT in peace. Clarkson later gets revenge by locking May in the trunk of his own car.
Uchuu Keiji Sharivan: The villains captured four young girls. Those girls were blindfolded, tied each other, and placed in the cliff. The villains threaten to kill them if Sharivan interfere their plan.
Warehouse 13: Happens to Artie of all people in the Season 1 finale. The gag is a NUKE that MacPherson put in his mouth.
A sketch on The Weekly with Charlie Pickering in the aftermath of the controversial raid by the Australian Federal Police on The ABC headquarters has Charlie waking up in a basement tied to a chair with a bag over his head. He is interrogated by three shadowy figures silhouetted by a bright light. After Charlie vows not to tell them anything, it turns that his interrogators aren't anything to do with the AFP or intelligence. They are actually Tom, Lucy and Adam, and they were just bored.
White Collar: Happens to Neal in season 4. Needless to say it resulted in much fangirling.