Well, assuming there's no Conveniently-Placed Sharp Thing nearby to cut the bonds, there's only one thing to do: Get attention in the hope of attaining rescue.
The simplest and most common (and often, the only) way to do this is to make noise. Banging on a wall or floor with bound feet, or making noise through a gag, are the most common. If the captive has a bit more freedom of movement, then knocking things over could work, or making a signal of some kind. If the captive is lucky, which happens the majority of the time, it'll be the heroes who hear the noise and come to the rescue. Sometimes, it's instead the villains, who then do a better job of restricting the captive. Other times, there's nobody around to hear the captive's attempts at rescue.
Note that merely struggling and making noise out of frustration is not this trope. Only if the captive is making noise with the goal of obtaining rescue, would it be Banging for Help.
If the captive is more savvy, he or she will bang in Morse code, which ensures that somebody will come by and realize what the message is and come to the rescue. Because, you know, Everyone Knows Morse (at least enough to recognize the alternating three-short-three-long SOS signal).
Has nothing to do with having sex to summon aid, although that certainly would be something.
- In the Pokémon episode "The Misty Mermaid", Misty's sisters do this after being bound, gagged, and stuffed in a closet by Team Rocket, who wanted to take their place in the play that was happening.
- Played for laughs in the Outlaw Star episode "The Strongest Woman in the Universe". Aisha tries to pose as a wrestler named Firecat, and during a locker room scene, the real Firecat bangs for help and manages to fall out of the locker she was left Bound and Gagged in. She tries to call for help but Aisha quickly stuffs her back inside.
- Happens several times on Detective Conan to alert Conan, who has Hyper-Awareness, that somebody's in serious trouble somewhere.
- Fullmetal Alchemist: when they got trapped together in a place where Pride was powerless, he pretended to play with Al's helmet, but his idle banging actually contained messages to his allies.
- In the manga adaptation for Kingdom Hearts II, DiZ locks Naminé in a broom closet to prevent her from interfering with Sora's awakening. Her banging is what caused Axel to rescue her.
- A variation occurs in the Astro City "Dark Ages" story arc. Seeking shelter at an arms cache during a citywide riot, Royal Williams finds his brother Charles dying from a gunshot wound. Desperate to attract the police despite the chaos, Royal fires off all of the weapons to try and warrant attention.
- An issue of Catwoman has the title character chloroforming a bartender in order to take the woman's place at a fancy party. The real bartender soon wakes up and manages to make enough noise that she is discovered tied up and gagged in a closet, blowing Catwoman's cover.
- Used in Marvel's Spygal one-shot. The title heroine discovers that a French businesswoman has been Bound and Gagged and replaced by an impostor after hearing banging noises and "mmph" sounds coming from a nearby closet.
- Marvel 1602, the Thing is Buried Alive in Doom's castle. Less this trope and more as a way to pass the time (and piss off Doom), he leans from side to side with enough force to echo in the castle.
- DEBS: Amy and the other DEBS are investigating a bank robbery. While passing by a closed door they hear a "Mmmmm" noise from behind it. When they open it they find the bank's employees tied up and gagged, and they "Mmmmm" again.
- Frog And Wombat, an independent kid movie about two middle school Kid Detectives who solve a murder, has "Frog" tied and gagged by her school principal, and using her toe to push a button on a walkie-talkie to try to get the attention of her friend "Wombat".
- Played unusually in U-571, as the German captive on their sub isn't Banging for Help, he's banging out Morse code: "I am U-571, destroy me."
- The ending of The Poseidon Adventure featured this as the way the band of survivors was rescued.
- What Peewit does after being bound and gagged by knocking things over in his room after After Torchesac/Oily-creep/McCreep steals the magic flute the night before in The Smurfs and the Magic Flute, alerting Lady Prattle.
- In an Italian movie about the Aldo Moro kidnapping, he hears a child bouncing a ball in the apartment above and starts banging on the ceiling with a broomstick to get attention. However the child's mother thinks someone is just complaining about the noise and tells the terrorists that she'll get the child to stop.
- In Dressed to Kill (1946), Holmes and Watson arrive at the Kilgore home to find it seemingly empty. Once inside, Holmes hears a banging noise and discovers the Kilgores' young daughter Bound and Gagged in the cupboard; kicking on the door to attract attention.
- The Adventures of Archie Reynolds has a hilarious variant of this. Amanda is Bound and Gagged in a crate and banging and "mmmphhing" to get attention. Archie is terrified of the banging, muffling crate for several pages, until he finally realizes "these might be human moans".
- Nancy Drew is especially notable in that she (in at least one instance) combines this trope with her knowledge of Morse code.
- The J.T. Edson character Doc Leroy, temporarily working as a lawman, was coshed and immobilised to prevent his interfering with a planned robbery. (The crooks didn't kill him as Leroy had plenty of the kind of friends you don't want to spend the rest of your life running away from.) He was reduced to banging on the floor of the hotel room he was shut up in, hoping to attract attention.
- The main character of What is the What does this when burglars tie him up in his own house. To alert his neighbours, he starts by kicking the floor, then moves on to kicking the door, which makes a good deal more noise.
- In Alfred Noyes's poem "The Highwayman", Bess, with no other way to make a noise loud enough to warn her lover of danger, shoots herself with the musket tied to her.
- In the Dan Brown thriller Deception Point, scientists Rachel Sexton, Michael Tolland, and Corky Marlinson are left for dead on an iceberg in the arctic by a team of Delta Force operatives sent to cover up the results of their investigation. Rachel uses an ice ax to bang out S.O.S. in Morse code to get the attention of the hydrophones listening hundreds of miles away. She doesn't believe that the trio can be rescued before they freeze to death, but she hopes that whoever finds their bodies will dig into the anomaly they were investigating. They end up getting rescued by the Navy submarine USS Charlotte, which happened to be three miles away on a highly classified lie-and-listen mission.
- In The Worst Witch in the episode where Miss Cackle gets tied up, gagged and left in the storage closet, when she sees Mildred and Enid flying in through the passage at the top of the closet, she starts making noise.
- In The X-Files, a bound and gagged Agent Scully bangs to attract the attention of a police officer when locked in the trunk of Duane Barry's car who kidnapped her. Unfortunately, this leads to the cop being distracted enough that Duane can shoot and kill him.
- In Dexter's fifth season, Lumen bangs on the side of the car's trunk when it stops at a red light. Unfortunately, the light changes, enabling her captor to speed off before the interested fruit vendor can properly investigate. But he does tell Debra of his suspicions that someone was in the trunk later, leading her to the villain's hideout.
- Vera: In "A Certain Samaritan", the Vict Im Of The Week is thrown off an overpass and lands on top of a truck passing underneath. He breaks his back in the fall and raps on the top of the truck in an attempt to attract attention. The truck driver hears the banging but ignores it and the victim dies.
- Wonder Woman: In "Fausta the Nazi Wonder Woman", a bound, gagged, and trapped in a crate Steve Trevor alerts Wonder Woman as to his whereabouts by kicking the crate and mmmmruphing through the gag. She beats up some mooks and rips open the crate to rescue him.
- Rachel from Tower of God bangs full of despair against a magical barrier that separates her from Baam, as he takes Headon's test. She is in fact trying to stop him.
- In the video for Street of Dreams by 80s metal band Rainbow, the hero's girlfriend, tied a chair, gagged, and locked in a closet, manages to attract her boyfriend's attention by kicking the door with the toes of her shoes.
- Dick Tracy was once held captive during World War II by a villain named Flattop. He hammered out a message with his feet in Morse code, which was heard and correctly transcribed by a young woman upstairs.
- In Town of Salem you can be silenced by the Mafia Blackmailer. Most people's response to this is to spam the Votes to not get hanged when people claim they are suspicious.
- In Dragon Age: Inquisition, Comte Boisvert can be heard letting out muffled shouts from inside a cabinet after an assassin ties him up and steals his clothes.
- In Ace Attorney Investigations 2, Sebastian Debeste, who was left Bound and Gagged in his own garage after being mistakenly kidnapped by his corrupt father's men, does this to get the attention of Edgeworth and Kay, who are in the middle of investigating another kidnapping case and are therefore around to hear him.
- Julie Yamamoto in Ben 10: Ultimate Alien does this after being bound, gagged and locked in a closet by Elena in "Revenge of the Swarm". It worked.
- Happened in "Which Witch is Which?", an episode of Scooby-Doo, Where Are You!, which had Daphne tied and gagged along with a sheet put on her. Her struggles and her mmmphing through her gag from under the sheet caught the gang's attention, whereas they otherwise might have ignored her.
- In the Superman: The Animated Series episode "Feeding Time", Superman bangs out "SOS" on the pipe that Parasite tied him to to get Jimmy Olsen's attention. He succeeds.