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.
The Avengers: 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 (1960's): The episode "Catwoman's Dressed to Kill". Catwoman orders an already bound Batgirl to be gagged to stop her backtalk.
Buffy the Vampire Slayer: Occasionally happens. Dawn, Buffy, Spike and others are get tied a few times throughout the series.
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.
CSI NY: Did it with Christine,Mac's girlfriend, in 'Seth and Apep',the NY half of the crossover where she was kidnapped.
Dexter: His playmates are mostly bound and gagged when he's having his... fun with them.
This happens to one of the Doctor's companions seemingly every other episode.
Romana gets tied up about five times in "The Androids of Tara," which must surely be some sort of record.
Rose gets bound in three of the first four episodes of series two of the new series. She is bound by Cassandra in "New Earth," then Chained to a Rock in "Tooth And Claw" to be eaten by the werewolf, then is bound to a torture rack in "The Girl In The Fireplace."
Adric and Turlough also got tied up, so at least the writers weren't being sexist.
Happens to the Doctor himself in "The Caves of Androzani," Part 3.
The Third Doctor is bound and gagged in Day Of The Daleks, as is Jo Grant.
Jack gets chained up during "The Last of the Time Lords"
Elementary did this most notably in "A Giant Gun, Filled With Drugs" to the daughter of one of Sherlock's old friends.
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.
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.
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.
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.
LOST: The season 2 finale saw Jack, Kate, Sawyer, and Hurley bound and gagged by the Others, though the gags were largely unnecessary.
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 Fuel or Distressed Damsel bent. It seems to be mostly coincidence.
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.
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.
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.