This is the one where a woman is giving birth, and a man (as it is Always Male) must coach her through the process. It may be played for laughs as the man pulls horrified faces at the sight of what's happening between the woman's legs, or it might be emotionally-charged melodrama.
It's implied that she would be in trouble without him, but the trouble is not defined as a specific medical emergency since the man is not a medical professional. At the very least, she is helped by his emotional support, even if he's a relative stranger to her; at the most extreme, it's implied that somehow she would not be able to give birth safely without someone telling her when to push.
If a doctor or midwife shows up, the guy is off the hook, and the birth usually takes place away from the camera.
The man is rarely the mother's significant other. Occasionally he is a potential significant other, and the two of them are drawn closer together in this unexpected intimate situation. He could also be a potential partner for another female character, who is afterwards impressed by his bravery and sensitivity.
Whoever he is, he's treated as a hero for having done this (even though all he did was hold her hand and tell her to push, and maybe "catch" the baby as it's born), and tends to be given more attention than even the mother. If he's not the father, he might be given impromptu "father figure" status (especially if there's no actual father to feel threatened about this), and be the first to proudly hold the baby while standing at the beaming mother's bedside. The baby might even be named after him.
Aversions would include: a non-professional woman assisting during another woman's labour, with no men present; or a woman giving birth alone, instinctively knowing what to do, and not needing any emotional support to keep her from panicking.
Can be subverted by having the man panic or even pass out while the woman just gets down to business.
Often combined with Screaming Birth and Locked in a Freezer. May or may not subvert Instant Birth, Just Add Water.
If you thought this was about some other type of delivery guy, you should look up the guy who visited nine months prior under Pizza Boy Special Delivery or Courier if the deliveries typically arrive in boxes and aren't infants.
Anime & Manga
In Barefoot Gen, the titular character's mother is pregnant at the start of the film, and the family is anxiously awaiting the birth of the child. Then Little Boy drops, and after a failed attempt at rescuing her husband, her daughter, and her other son from their burning house, the stress causes Kimiko to go into premature labor. Six-year-old Gen tries to find a medical professional, but all the doctors and nurses are too busy attempting to treat the burned bomb victims. Thus Gen is forced to deliver the baby himself.
Played for Laughs at DC Nation when Sue Dibny went into labor. Ralph was busy with a rogue, Mid-Nite was stuck in surgery, so little Allanah Dibny was delivered by Eel "Plastic Man" O'Brien, Hal Jordan, Martian Manhunter, and Wally West!
Plastic Man:Whoa, Sue...not the way I wanted to look up your skirt!
In Through A Diamond Sky, the heroes are making their escape from the Resource Hog base on a stolen Recognizer when the Iso scout Kanna goes into labor. As everyone else is occupied, Flynn gets the short straw.
John Ford's The Three Godfathers has three main male characters, so only one has to go in and help with the birth, which takes place offscreen (though the man still knows nothin' about birthin' no babies.) Miraculously, the baby is still named after John Wayne's character. (Well, named after all three of them, but Wayne gets the first name.)
Theo does this for Ki in Children of Men, in a rundown building in the middle of a battle-torn refugee camp. She names the baby after his son.
In Ice Age Dawn of the Dinosaurs, Diego has to coach Ellie through her delivery... while fighting away hungry raptors.
Pauline plays Borovnian Emperor Charles doing this for Empress Deborah (Juliet) for the birth of Diello in Heavenly Creatures. Juliet enacts contractions and proper breathing pretty convincingly in a semi-Screaming Birth. Charles is pretty inept, telling his wife to push between contractions.
Played with in the Doctor Who episode "Amy's Choice" where a heavily pregnant Amy pretends to go into labour, and the Doctor dives down, holding his hand beneath her legs as if he was going to catch a football.
Star Trek: The Next Generation episode "Disaster": When the aforementioned disaster left groups of people trapped in different areas of the ship, it fell to Worf of all people to assist in the delivery of Keiko O'Brien's daughter. It helped cement Worf's character as lackingin interpersonal skills after he yells "Push!" for the umpteenth time, Keiko snaps back with "I AM pushing!" and his line "You may now give birth." The baby is named Molly Miyaki Worf O'Brien in his honor. The birth gets a Call Back in Deep Space Nine: when Worf is told that Keiko is having another baby, his immediate reaction is a panicked "Now!?"
In the classic Star Trek episode "Friday's Child," Kirk and McCoy protect a woman who is pregnant with the heir to the leadership of her people. She gives birth in a cave while hiding from their enemies, and McCoy assists (he's a doctor, so this takes place off camera). At the end of the episode, Bones announces that the baby was named Leonard James Ak'aar, after both of his mother's protectors.
Superman's done this loads of times, including once in Lois and Clark, when the father says afterwards, "I've just thought of the perfect name." There was also a story in the comics where he saved a guy from suicide, left him with the expectant mother while he rescued someone else, and came back to ask the guy if he still thought he'd never achieved anything in his life.
Community - Happens to Abed without anyone noticing in a series of Funny Background Events in season three episode two. When Shirley asks what he's been up to all day, he replies "Nothing much." When Shirley is giving birth, Abed tries to put his experience to use (with more lampshade hanging on how no-one knew what happened) but it eventually falls to Britta.
Abed: At each contraction, you need to tell Shirley to push.
Britta: That's it?
Abed: Well, don't tell any doctors I said this, but at this point in time the bus pretty much drives itself.
Happened in Malcolm in the Middle, with Francis being forced to help deliver his own mom's baby, at one point being told "stick your hands inside of Mommy!" Afterwards, she tells him how it was the best thing he's ever done for her - and that he can go vomit now.
On Taxi, Alex Reiger is forced by circumstance to deliver a baby in the back seat of his cab (The father/coach couldn't handle it). The parents wanted to name the baby after him... until he told them his name.
The classic subversion, even though the birth doesn't actually happen on screen, is from I Love Lucy. Ricky and the neighbors are practicing what they'll do when the baby is about to be born: calling the doctor, grabbing Lucy's luggage, helping her on with her coat and heading out to the car, all with perfect calm and grace. Then Lucy waddles into the room and says, for real, "Ricky, this is it!" Hilarity Ensues as Ricky and the neighbors run around like chickens with their heads cut off, and Lucy, looking uncomfortable but still keeping a cool head, has to remind them of what has to be done. To top it all off, they initially leave Lucy behind.
Home Improvement: Tim, Jill, and mom-to-be Heidi got stuck at a pit stop when labor hit. Jill and Tim coached her through it, and Tim gave up his soft and warm jacket for the baby.
When Bailey on Grey's Anatomy had her son she pretty much gave up when it came time to push, since her husband was in surgery at the same time. She ended up being talked to her senses by George, who then proceeded to coach her through the delivery. She gave her son the middle name George.
Played with when Daphne enters labour in a vet's surgery. The vet himself is next to useless, Niles' attempts to keep her calm by coaching her through her breathing exercises only result in him passing out as a result of a fit of hyperventilation, and it falls upon a woman in the waiting room who happens to be a doctor to take charge of everything.
In another episode, Niles, Frasier, and Martin get a cab. The female cabdriver asks if they've heard any of the "giving birth in a cab" stories that have been spoken of as folklore amongst people. After the three men respond, the driver, in an inversion of the typical stories (where the passenger is pregnant and the driver must deliver the child as she goes into labor), explains that it is going to happen right now and goes into labor herself. The three men do their best to help her, with varying degrees of competence (Frasier tries but is ultimately useless, Niles is completely incompetent, asking why the meter is still running at one point, and Martin, having been a father himself and a retired police officer who has had to deliver babies a couple times, doing the best job of the three). Both mother and child make it to the hospital safely. Niles considers fatherhood after the event, spending the rest of the episode trying to raise a sack of flour as his son, directly or indirectly inflicting enough harm on the "child" to kill or seriously injure him at least twice (including but not limited to impaling with a sharp instrument and third degree burns). By the episode's end, Niles decides that fatherhood isn't for him at this time, though after what happened to the sack child many viewers would probably be inclined to suggest a vasectomy instead.
Niles & Frasier are medical doctors, for crying out loud. Sure, they're psychiatrists, but they would have had to go through maternity rotations in medical school/internships.
Used several times in Stargate SG-1, always with the character of Daniel Jackson. He played Delivery Guy to his missing wife, who he'd just found heavily pregnant with Apophis' child - making him deliver the Big Bad's kid and heir, as well as to a woman giving birth alone in a temple. Seems he's either got his hands up there or... something else.
Teyla of Stargate Atlantis didn't need much support despite giving birth while stuck on the enemy's ship, but a very reluctant McKay does overcome his nerves to 'catch' the baby. She still names him after someone else.
On LOST, Claire went into labour in the middle of jungle. Technically it's Kate who eventually delivers the baby, but more or less panicked Jin and Charlie provide support.
Averted on The X-Files, where it is a fellow female agent, Monica Reyes, who must help deliver Scully's baby while hiding from those who want to kidnap the child.
Primeval season 3 episode 3, where the B plot is that Abby has to deliver a baby when locked in a room with Nick and a pregnant woman.
In one episode of Law & Order: Special Victims Unit, a pregnant woman who has been kidnapped by her ex-husband has been found by Elliott. She is scheduled for a C-section because the placenta formed over her cervix (meaning the baby would otherwise burst through it a la Alien and cause her to bleed to death). Elliott calls an ambulance, but the baby is coming too quickly. He delivers the baby (using knowledge gained from being present at the births of each of his own children), but the mother does not survive.
Averted with Kathy Stabler who is given emotional support by her husband's partner Olivia Benson while on the way to the hospital.
Kyle XY has an episode where Kyle must help a stranger give birth on the side of the road. It had to be him even though there were others with him because he's so smart that everything comes to him naturally.
A short film from the Sci-Fi series Exposure had a man attempting to be the first suicide of the 21st century instead wind up delivering the first baby of the 21st century. Judging from his expression the next morning after seeing his picture on the morning paper and people recognizing him, he feels like everything turned out all right.
Played with in Falling Skies. When Sarah gives birth, Anne, who despite being a pediatrician is the only doctor they have, is set to deliver with Margaret there for emotional support. When it becomes apparent that the baby will be born breach, Anne admits to Captain Weaver she does not know what to do. He reveals that he helped deliver his babies both of whom were born breach, and takes over.
Farscape: The usually incredibly calm, cool, and collected Aeryn Sun needs John's coaching to get through her delivery as she really doesn't seem convinced she can do it. They were in the middle of a battle and getting shot at at the time so a little panic seems pretty warranted.
The NCISChristmas Episode "Newborn King" has Gibbs having to deliver an army lieutenant's baby which is the focus of a conflict between the Department of Defense and a tribe of Afghan natives over land rights and inheritance.
Ziva is present, but the woman wants a Marine to deliver the baby, so Ziva leaves to fight off the mercenaries.
On JAG, Admiral Chegwidden did this twice in his office.
In the Fringe episode "Bloodline", Henry the cab driver ends up having to deliver Fauxlivia's baby on the floor of a clothing store in Chinatown.
A variation in Psych. Chief Vick gets to a hospital before the baby is born, but her husband is stuck in traffic, so she asks Lassiter to stay with her.