In Children of Men, almost all of humanity has been rendered sterile, and society has collapsed into violent chaos.
The movie Daybreakers strongly implies this for most of the population, as the vampires, who compose 95% of the population, do not age or procreate. Another 4% are humans kept as stock to produce blood to feed the other 95%. The other 1% may have kids, but they are hunted down relentlessly by the vampires (who need more blood).
Chitty Chitty Bang Bang features a Ruritania in which the Child Hater rulers have actually outlawed children. Yes, it makes no sense. It's not clear what the government does to the children, except that they're rounded up by the infamous "Child Catcher".
Early in Belgarath the Sorcerer, Belgarath encounters a camp populated entirely by old people. They turn out to be the people who refused to follow Gorim to Ulgo, and were cursed with sterility as a result. They're just waiting to die off, and Belgarath finds the winter he spent with them very depressing.
New World in the Chaos Walking trilogy. Due to the fact that all the women in Prentisstown are dead, there hasn't been a child there in 13 years - not since the main character Todd was born.
In Peter S. Beagle's The Last Unicorn, a town has stopped having children ever since they heard a prophecy that one would bring down the king and end their prosperity. They live in dread of that day. At the end, after the old king has been brought down, the magician Schmendrick urges them to have children — it might help.
The Declaration Trilogy by Gemma Malley is set in a world where scientists have discovered life-extending drugs. However, a corrupt government is using the drugs to cling to power and prevent a younger generation from challenging them. Under the pretext of preventing overpopulation, strict laws have been passed, stating that no-one may reproduce unless they "Opt Out" of taking the drugs; even then, they are restricted to one child each. Any children born to parents who have not "Opted Out" (or who have "Opted Out" but already have a child) are labelled "Surpluses" and are taken away from their families to be raised in grim institutions. As very few people choose to "Opt Out", the result is a society where children, whether they were born legally or not, are greatly mistrusted.
Ashes by Ilsa J. Bick has more of a "Teenager-less Dystopia". In this apocalyptic world, some sort of electromagnetic pulse turned most of the teens into zombies and killed most adults. As a result, most of the survivors are the elderly or children under 12.
In "The Handmaid's Tale" by Margaret Atwood, future Earth is so irradiated that most humans are sterile, and the births that do happen are usually "Un-Babies" with severe defects. This leads to a theocracy in which the few remaining fertile women become sex slaves for powerful men.
Live Action TV
In Stargate SG-1, the Aschen Confederation offered the people of the planet Volia (P3A-194) a cure for a terrible disease on their world. However, the vaccine also resulted in sterility. A once thriving world of millions was reduced to chaos and riots, and then to a peaceful but empty world, with a few thousand apathetic residents and automated machines tending farmland. An earlier episode portrayed a Bad Future in which the same race was in the process of doing this to Earth.
In "Past and Present", SG1 arrives on a world where everyone is a young adult with amnesia and, while there are pictures of older people and children, they are nowhere to be found. It turns out that a Mad Scientist's experiments with longevity caused everyone to revert to a younger age, making the elders young adults and the children nonexistent.
The main driver for The Outer Limits episode "Black Rain". In the episode, a rain of some toxin causes people to become mostly sterile, resulting in this.
At the beginning of Half-Life 2, the Combine have been using a suppression field to arrest human reproduction for years. The empty playground pictured above has the faint, ghostly laughter of children to reinforce the creepy-factor. Blowing up their Evil Tower of Ominousness at the end of the game removes the suppression field.
Fallout 3's DLC The Pitt is affected by a contagion that disfigures and sterilizes the residents, or worse, makes them go crazy or become Trogs. The only child in the area is Marie, the infant daughter of Lord Ashur, and she has an immunity to the TDC (Troglodyte Degeneration Contagion) that raises hopes for an eventual cure.
It's not completely childless - one in a thousand survive - but this is pretty much what happened to Tuchanka in the Mass Effect games when the genophage was deployed, and the krogan culture has spent the last 1500 years spiralling below the Despair Event Horizon as a result. It's telling that one of the Golden Ending slides for the krogan, if you cure the genophage, depicts them with children again; it is the happiest you will ever see them.
In Digital Devil Saga this forms a mayor plotpoint and reveal at the end of the first game giving both the characters and players a mayor clue that something is seriously of about the Junkyard. The second game averts this trope entierly.
Lupa:Have you ever seen a child here in the Junkyard?
The Easter Bunny Is Coming To Town features the adults-only city called Town, which oddly is ruled over by a child king and his older aunt. There's a subversion involved in that near the Town is the children-only city called Kidville.