Kid Has a Point

In Real Life, it is generally accepted as a fact that people grow smarter and wiser as they get older. Therefore, whenever a younger character turns out to be right over an older character, it's considered shocking or hilariously ironic. This trope can come into play if the child in question is Wise Beyond Their Years, but is brushed off or ignored because they're still Just a Kid. It needn't be limited to children vs. adults either; it's just as apt to arise in debates between adults of different generations, complete with references to the age gap.

This may be a case of Truth in Television to some degree. A younger generation often brings a fresher perspective to a situation than their elders, and they may also be more willing to question traditional concepts. What is more, novelty has no particular stigma for them, since for them most things are new.

Compare Adults Are Useless.

Not Now, Kiddo is the inversion of the trope.

Anime And Manga

 * In Detective Conan, Shinichi continues solving mysteries even after shrunk into the body of a child. While he has trouble getting adults to listen to him, he figures out how to trick the police into finding evidence by acting like a curious child.

Comics
"Molly: If magic can't make the dead lady breathe again, can it show us her memories?"
 * In Runaways, Molly is the youngest of the group and treated like a little sister by the other kids, but can be very insightful. One notable instance is when Gert's future self appears before them and dies before being able to answer any of their questions, and Nico can't use magic to revive her.

"Gert: From the mouths of babes."

Film

 * In the movie 'Gregory's Girl' by Bill Forsyth, Gregory's younger sister Madeline is a classic example of this trope.
 * The movie Sleepless in Seattle is based on this premise. Jonah wants his sad father to remarry, so the boy takes the initiative to call a radio psychiatrist, setting off the whole sequence of events.
 * A big part of Chicken Little is that Chicken Little is right about the strange things going on in town and the townsfolk (especially Chicken's dad) need to listen to him about it.
 * In How to Train Your Dragon, Hiccup knows that dragons aren't as dangerous as his village believes, but has trouble convincing his father.

Literature

 * The Emperors New Clothes climaxes when a child utters the obvious truth that the Emperor has no clothes.
 * The Baudelaire Orphans repeatedly in A Series of Unfortunate Events.
 * The Bible originated the expression, "Out of the Mouths of Babes" that relates to this trope.
 * This is a recurring theme in the Deryni works generally; younger people are seen to question and doubt old ideas: the fears promulgated by the Church hierarchy and the received wisdom (untested) of the High Deryni Lords of the Camberian Council. Some of the younger people even act on their different notions of the proper and the just. In particular:
 * Deryni Checkmate: During the meeting of the Curia on the Corwyn Interdict, Archbishop Corrigan (then Archbishop of Rhemuth and Loris's ally) reacted to the defiance of the younger Cardiel and his allies by "[throwing] up his hands in dismay. 'O Lord, deliver us from men with causes! Are we now to be schooled by our juniors?'"
 * High Deryni: In a meeting of the Camberian Council, Tiercel deClaron (the youngest member) mounts an eloquent defence of Morgan and Duncan when two other members deride them for being half-breeds. Tiercel starts with the proposition that they should be sought out "on bended knee, begging them to share their great knowledge with us" (referring to the pair's rumoured rediscovery of Healing, a talent lost for some two centuries). He goes on to suggest, based on what they know of the powers, that being Deryni may be an all-or-nothing proposition like other traits. After a long silence, Barrett deLaney quietly says, "We are well instructed by our juniors."
 * Talen from the Elenium has a knack for figuring out things before the adults.
 * Gher from The Redemption of Althalus. He's not just The Smart Guy, he's a young smart guy.

Live Action Television

 * Wesley in Star Trek: The Next Generation had such occasions, then started doing it a little too often, leading to some fan backlash.
 * Once the rest of the Power Rangers Turbo cast changed over, lone holdover Justin tended to be the first one to figure out what Divatox's Evil Plan of the Week was.

Video Games

 * World of Warcraft: Anduin Wrynn is calmer and more diplomatic than his father, which sometimes leads to this trope.

Western Animation

 * The protagonists of South Park tend to invoke this in episodes with An Aesop.
 * The Simpsons. There are a lot of episodes where Lisa manages to come up with a solution where adults have failed. She is usually more intelligent than Homer as well.
 * My Little Pony Friendship Is Magic: In the episode "Bridle Gossip", Apple Bloom is the only one to assume that Zecora isn't evil, contrast to the Mane 6 who are much older than her and guess Zecora is evil. Turns out Apple Bloom's assumption was correct all along.