Screening the Call

The Hero would be happy to answer the Call to Adventure. After all, he's been waiting in the Call Receival Area, waiting for the message to appear - but he learned that someone's been clearing the voice mail behind his back. It seems that some well-meaning family, friends or loved ones are preventing the Hero from catching the call.

Why? Maybe the Hero's Love Interest knows the The Hero's Journey is dangerous and, well... Maybe the Hero has really overprotective parents who don't want their child harmed. Maybe some tragedy has occurred in the past and it's known that adventure runs in the family. Maybe the Hero is in store for some really nasty fate. Maybe the town is uncomfortable with the Hero's Stock Super Powers and would really rather he were just normal. Maybe they have an interest in making sure Nothing Exciting Ever Happens Here (after all, adventure is really bad for property values). In really extreme circumstances, those Screening the Call might take the Hero out of the equation.

Eventually, those well-meaning but obstructive people will discover that The Call Knows Where You Live, and will thus be forced to give in (assuming the Call doesn't exact revenge by killing them off first).

Anime and Manga

 * Dragonball Z: Good luck getting Gohan to help save the world if Chi-Chi's nearby.
 * Puella Magi Madoka Magica: Akemi Homura is actively trying to prevent Madoka from becoming a Magical Girl.
 * In Suzumiya Haruhi, the rest of the characters are constantly working to keep Haruhi Locked Out of the Loop regarding her own powers. They have a very good reason, though.

Fan Works

 * Played with in With Strings Attached: After Ringo crops up psychic and John starts flying in front of the others, the Fans decide they'd better get the other two some magic to prevent group friction. They maneuver George to his shapeshifting ring, but before they can deal with Paul they're kicked off their computer by an official because their school is closing for Winter Solstice Vacation. Paul spends an undetermined amount of time drinking and jealous because of this, though the Fans finally do get to him once they return to school.
 * The Fan Fiction White Devil of the Moon, has Fate preventing the Sailor Senshi from finding Nanoha because a) Nanoha has just been badly injured and is a workaholic, and b) if Nanoha gets involved, she will overwork herself trying to solve the Senshi's problem, putting her back in the hospital.

Film

 * Uncle Owen and Aunt Beru seemed to be doing this to Luke Skywalker in Episode IV of Star Wars, at least before the Empire caught up with them. Uncle Owen was the staunchest proponent of Luke staying home despite Beru's insistence that "Luke's just not a farmer, Owen. He has too much of his father in him." Owen's answer: "That's what I'm afraid of." We're initially led to believe that they're afraid Luke's going to get himself killed just like his father, but after a certain reveal in The Empire Strikes Back, we learn that what they're really afraid of is the possibility that Luke might fall to the Dark Side and go evil like his father.
 * In the latest Transformers movie, Dark of the Moon, Sam's new girlfriend Carly is playing this trope when Sam starts assembling the clues to a new adventure. She would prefer that he leave his dangerous ways in the past while he safely basks in their glory in the present. She fears that if he goes off to war again that it will be a repeat of the tragedy that claimed her brother. Unfortunately for her when she leaves Sam she unwittingly walks straight into the thick of the plot and becomes a Damsel in Distress.
 * In Be Cool, Raji literally does this to Elliot when he deletes messages left for him by Chili. He'd prefer to keep Elliot as his muscle forever rather than let him embark on a movie career.

Literature

 * Harry's foster family, The Dursleys, in the Harry Potter and the Philosopher's Stone.
 * This happens all the time to Harry Potter; it's not just the Dursleys. In the second book, it was Dobby; in the third, the Ministry, and in the fifth, Dumbledore.
 * Lyra's mother in His Dark Materials hides her in a cave and keeps her in a drugged sleep to prevent her from fulfilling her destiny.
 * In the first book the Headmaster of Jordan College tried to kill because he knew the man's experiments would instigate the conflict with the church and that Lyra would be drawn into it.
 * In some versions of Peter Pan, the father was once a Lost Boy and didn't want his children to leave him.
 * In The Rowan, all the psychic Primes who handle interstellar teleportation were trained by the neurotic, agoraphobic and overbearing Siglen who telepathically impressed her own inability to handle personal travel into all the other Primes, making travel off their homeworlds a mind-scarringly traumatic experience and leaving The Rowan unable to assist her distant lover in a Bug War that threatens to kill his entire planet. Luckily, The Power of Love leads her to ovecome the effects by realizing that it's just psychological baggage, not an inherent trait of Primes.
 * The overprotective parent flavor shows up in the Codex Alera, though it's at least partially an accident.

Live Action TV

 * On Chuck, it was revealed that Chuck was targeted for CIA recruitment during college, but his friend Bryce got him expelled so he wouldn't get involved with spy work. Later on, it becomes apparent that . Needless to say, it doesn't work.
 * Buffy is adamant about keeping Dawn out of combat. That's all well and good, but considering Dawn's a MacGuffin Girl and the sister of the Slayer who is quite literally bound by destiny to be in the wrong place at the wrong time and fight the evil that results, it becomes fairly obvious to everyone that trying to keep Dawn out of danger only serves to make her an easy target. By season 7 and the comics, Dawn has received training, and Took a Level In Badass, becoming a hell of a lot more useful and less likely to be kidnapped.

Tabletop Games

 * The Seers of the Throne, the major antagonist group in the roleplaying game Mage: the Awakening, make it a point to interrupt Awakenings if the mage won't throw in their lot with the Seers. According to the game's Karma Meter, this is a very bad thing.
 * The more benign version of this is done by the Guardians of the Veil, who (quite understandably) believe Awakening should be a privilege, not a gift to be handed out willy-nilly. As a result, they create a sort of pseudo-conspiracy, called the Labyrinth (a trail of supposedly world-controlling organizations and conspiracies that also happen to be complete bunk) meant to mislead people only in it for the power away from Awakening and people Genre Savvy enough to realize they're being fooled towards it. More than one Guardian is proof that it works.

Video Games

 * In Psychonauts, Raz's father forces Raz into rigorous acrobatics training in order to keep him from mastering his psychic potential. Not because he's overprotective but due to his prejudices against psychics.

Web Comics

 * In Girl Genius Agatha's uncle gave her a locket that  and her parents aren't who they seem.
 * But without it, she would have been killed by a mob of angry villagers...or ...or would have been the cause of a civil war that she would have been very unlikely to survive. At least now, she has the resources and ingenuity to survive what's going to be thrown at her (hopefully).
 * It was also a protection from opportunists (other than "The Other") who might use her as a political pawn, as they did with a more distant relation. Punch and Judy further delayed the call by sticking her in a university, where her mediocrity would stand out in contrast to all the Sparks while forcing her to learn the hard way what comes naturally to them. When the Power Nullifier came off, she had all that education at her disposal, and she was ready for the call.

Western Animation

 * Toph's parents in Avatar: The Last Airbender. Aang and friends invite her to join their team, but her parents (who can't comprehend that their blind daughter is far from helpless) want to keep her isolated and protected. Luckily, it's hard to keep tabs on the world's greatest Earthbender.
 * Well after she leaves, Toph's parents still can't give up on keeping her out of the adventure; they hire a pair of highly skilled adult Earthbenders to find Toph and bring her back. The Earthbenders do find her... but then she kicks their asses and sends them back in their own steel box that was meant to hold her. By doing something thought to be impossible.
 * In The Simpsons, one of the earlier episodes has Marge trying everything possible to keep Homer from going to a big festival because he always gets drunk and "Ruins Everything." There's even a framed newspaper article on the wall with the headline being "Local Man Ruins Everything!" In the end, it doesn't work, and Homer finds out about the festival.