Mama's out for a stroll with little junior in his Baby Carriage. Too bad she's wandered into a Chase Scene!
This trope describes the phenomenon wherein, if there is a car chase, there will be a woman pushing a baby carriage (aka, pram or bassinet). In Real Life, you will never see as many women pushing baby carriages down the street as you will during a car chase in a movie or TV show. Obviously, this device works because the idea that a baby might be harmed as the result of a chase adds instant Drama. Of course, don't expect the drama to last long. It's usually just a temporary distraction, and both drivers will be able to swerve around said Baby Carriage.
In older comedies, nothing much was thought of having the baby actually get hit, even by the protagonists.
Sometimes subverted by having the protagonist horrified that he can't avoid hitting the carriage — only to find, as the carriage tumbles over the hood of the car, that it didn't contain a baby at all, just groceries or something equally innocuous (think Speed: "They were only cans!").
See also Fruit Cart and Cardboard Boxes for other stock obstacles that will get in the way of a Chase Scene, no matter how improbable their location may be.
Anime & Manga
In the anime Ergo Proxy, Vincent Law is attacked by a proxy in a crowded plaza. Raul Creed's wife is killed in the melee and the carriage carrying their adopted son is bumped and begins to roll down a flight of stairs. When we next see the carriage in the aftermath, it is lying on its side at the bottom of the stairs with blood pooling out of it.
Probably the definitive Odessa Steps/Baby Carriage scene is the fight in the station in The Untouchables. Kevin Costner had to make a Sadistic Choice between dropping the baby carriage down a flight of stairs or shotgunning a mafioso. He dropped the carriage, but fortunately, Andy Garcia was on hand to save it. By stopping it with his legs, while still shooting some bad guys. And the baby is okay in the end.
Brilliantly sent up in one of The Naked Gun movies during a dream sequence ("MMMMYYYY LLLLLAAAAAWWWWNNNNMOOOOOWWWWWWWEEEEERRRRR"). It gets bonus points for Nordberg trying to spike the baby after saving it.
Done with a twist at the beginning of Ghostbusters 2, with the carriage as the object of the chase instead of an obstacle. After rolling through a puddle of psycho-reactive pink slime, the carriage speeds away from Dana with Oscar inside as if propelled by a motor. She gives chase as it narrowly avoids several collisions, careening down sidewalks and through streets, finally stopping dead inches from being rammed head-on by a speeding city bus.
Subverted in Speed where Annie is desperately trying to keep a bus above 50 miles an hour and can't dodge a pram, smashing it to kindling. She is suitably horrified until Keanu Reeves notices that there was no baby in there, only cans, and the 'mother' was actually a homeless woman.
Subverted in the opening scene of The Soldier (1982). A woman with a baby carriage steps out in front of a limousine and is promptly run over. She turns out to be a terrorist (the baby carriage is full of weapons) trying to get the vehicle to stop so it can be ambushed.
Played straight in The Three Stooges short Grips, Grunts and Groans. While running from some train depot guards, the Stooges knock over a baby carriage - that contains a baby - and use the commotion of two women panicking over the injured infant to hide from their pursuers.
Subversion: In Batman Forever, the Batmobile is stopped mid-pursuit by an elderly crone pushing a baby stroller. After the vehicle screeches to a halt, the "Old Crone" whips off a shawl to reveal Big Bad Two Face, who then takes a rocket launcher out of the baby carriage.
Averted in Anne Fine's All Bones and Lies. The protagonist, Colin, is introduced to a single mother and her baby daughter when a car crashed into her baby carriage throwing the baby through the air. Colin's sister reached up and plucked the baby from the air, randomly saving her life. Both the mother and Colin take a long time to get over how nearly the baby died.
An episode of Power Rangers in Space had a variation: In the episode "Silence is Golden", The Psycho Rangers have Applied Phlebotinum set up to hone in on the sound of the Rangers' voices within Angel Grove. So Cassie is hurrying back to base as silently as possible when she sees a baby carriage about to fall down a flight of concrete stairs. She struggles between protecting herself and warning the mother, but what other choice does she have...? (Besides morphing in public and rushing up to save the kid herself as the Pink Ranger, anyway.)
In the first season of Charmed, there was an episode where a reporter sent an empty Baby Carriage out in front of an oncoming truck in an attempt to get Prue to use her powers. It kind of worked.
In the Doctor Who episode "Human Nature", when the Tenth Doctor is in human form to hide from the Monster of the Week and has no idea of his real identity, one of the hints of his Hidden Depths comes when he realizes a piano is about to fall on a baby carriage (two cliches for the price of one!) and sets off a Rube Goldberg-like sequence of events in time to stop it.
The Torchwood episode "Sleeper" shows a young mother who's really an alien sleeper agent who, upon being activated, walks away to carry out her mission and leaves her baby's pram to roll into the road. We hear the baby crying, followed by squealing brakes and a crash.
In an early episode of Teen Titans, "Final Exam", this is one of the disasters staged by bad-guys in training Jinx, Gizmo, and Mammoth to lure the Teen Titans into an ambush: "Aren't baby carriages supposed to have babies in them?"
In an episode of Codename: Kids Next Door (Operation DIAPER), a baby carriage rolls down a flight of stairs during a fight with a group of tooth-stealing babies. Number 3 chases it and catches it at the last moment, only to get punched in the face by the occupant.
Spoofed in a Halloween episode of The Simpsons. Homer's ghost has twenty-four hours to do a good deed to get into Heaven. Just when he's almost out of time, he sees a carriage going down a flight of stairs and picks up the baby just because he's annoyed with its wails. The baby's mother believes it to be a miracle. Too bad for Homer that St. Peter wasn't looking.
Another episode features a boat chase in which Wiggum has to avoid a woman jet-skiing with a baby carriage.
Subversion: The film The Triplets of Belleville spoofs the trope by having the car actually crash into the baby carriage and self-destruct — thanks to the remarkable heft of the baby.