Panicky Expectant Father

My goodness! My gracious!
When will this day be done?
Will it be a girl

Or will I have a son?

—Dexter's Dad, Dexter's Laboratory

When the Delivery Guy is the father of the baby, and has been preparing for this for the last nine months, he's often every bit as unprepared when the time comes as some random guy would be, and usually a lot less calm. Sometimes he's overprepared, so that he's still reading his checklist while his wife is having a Screaming Birth, sometimes his mind just goes blank at the thought he's going to be a father. On being told by his partner that the baby is coming, he will often charge off immediately to the hospital only to return a few seconds later to collect said pregnant partner. A comedy trope. When they finally get to the hospital, expect the wife to have to push said husband in to the building in the wheelchair, instead of the other way around, since by this point he's likely fainted, hit his head, or possibly fell down the stairs in a panic.

Frequently, the Panicky Expectant Father is given something ostensibly helpful to do, with boiling water and finding clean sheets being a fairly common task, or he's shown pacing outside the delivery room, often smoking like a chimney. This may be a way to indicate the progress without having to actually show the woman in labor.

Examples of Panicky Expectant Father include:

Anime and Manga

Minato in Naruto. In his case, he's got very good reasons to panic: his wife Kushina is the host of the Kyuubi, and childbirth is the moment in which the seal containing said Sealed Evil in a Can is at its weakest; if it ever broke, Kushina would die and the Kyuubi would be unleashed. And it happened. Sort of.

Comic Books

Reed Richards was acting a little like this when awaiting his first child's birth (compounded by feared complications caused by Sue's exposure to cosmic radiation and all that), but he had nothing on the guy whose wife was in the next ward, who fainted when told he was the father of twins.
Gaston Lagaffe does the chain-smoking-while-pacing-round-and-round version when waiting for his turtles to hatch.
- Fantasio does the same thing when Gaston is in the hospital after swallowing the prize from a box of candy.
Tobias Knopp in one story by Wilhelm Busch, when his daughter is born.

Fan Works

A common feature (but usually played for drama) in many, many, many, many, many Avatar: The Last Airbender fanfics in which Zuko becomes a father.
In this Fallout: New Vegas fic, Arcade and Veronica (who are both gay) sleep together after getting very, very drunk. Pregnancy ensues. To say Arcade becomes a Panicky Expectant Father is putting it mildly.
In Spy & Pyro, a Team Fortress 2 fan film, Spy and Pyro end up having a child, at which point Spy is seen nervously pacing outside the hospital smoking far too many cigarettes.

Literature

Adam's father in Good Omens is kinda like this. Lampshaded, even: "A man with 'expectant father' written all over him." (So of course, they swap his child with the infant Antichrist.)
In the Belgariad, Garion pretty much loses his mind during Ce'Nedra's labor. He gets sent away to make himself useful.
- By the time she gives birth, he's chopped several cords of wood and is considering how much wood he could get if he destroyed the woodshed...
Johnny Nolan in A Tree Grows in Brooklyn goes out, gets drunk, runs home to mother and fails to show up for his work as a school janitor; the pipes freeze and the school is flooded, and, naturally, Johnny loses his job (and the already poor family's only source of income). Also qualifies as an Epic Fail.
Hemingway's "In Our Time" plays this as darkly as possible: the expectant father kills himself "offscreen" during a complicated labour. The doctor and his son only realise this when the birth is finally over.
Ephraim Kishon once wrote a play about three of them (all named Kohn), and confessed having been this too.
Berrynose in Warrior Cats, who tries to rush his mate off to the nursery when he finds out that she's pregnant.

Live Action TV

Del Boy Trotter over the birth of Damien in Only Fools and Horses seventh season finale "Three Men, a Woman, and a Baby".
Ross, at the birth of Ben in Friends.
In "Bones", Hodgins completely loses it. Both times.

Hodgins: Okay, uh--baby! Baby! BABY!

Turk, at the birth of Isabella in Scrubs, eventually ends up trapped in an ice machine. The other births have been aversions or subversions: JD is too concerned with the realisation he needs to break up with Kim to panic too much at the birth of Sam. Dr Cox seems to have been fairly calm about the birth of Jack (probably because he didn't know the baby was his), and when Jennifer is born, we only see his concern about people associating her birth with Laverne's death.
Steve, at the birth of his unnamed child in Coupling.
Ricky in I Love Lucy.
Lost subverted this. In the flashbacks (flashforwards?) we see Jin running around buying gifts for a newborn baby, which we assume is his and Sun's child in the future. Turns out that Jin is actually buying a gift for the newborn child of his boss's client in the past and he is actually dead in the future and does not see his child being born, except he's not really dead.
Rob Petrie in The Dick Van Dyke Show.
In Full House when Rebecca starts having contractions, Jesse declares he's "not going to be like one of those jerks who panics when his wife goes into labor" and calmly goes to help her pack... by pulling an entire rack of formal wear from the closet. Even after that he's still calm and Becky even plays along before revealing she'd already packed a bag.
Vinton on Mama's Family: He totaled his truck and Mama's car all in his attempt to go to the hospital, forgetting the pregnant Naomi.
An Argentinian Comedy-Soap called Carita Del Angel (I probably got the name wrong) parodied this. One of the main characters is expecting his second child in a waiting room, showing all symptoms of a Panicky Expectant Father. He gets in a conversation with another man who looks positively bored. He explains that he was just as excited with his first two children. After that, he got used to it. The one he was waiting there was his 11th.
Subverted in an episode of Firefly where one of Inara's friends goes into labor while the crew is there to help fend off the father of her baby, and Mal...reacts.

Mal: Oh - it's starting - Okay. It's starting! No one panic, it's gonna be fine!
Simon" I got this one, Captain.

- Of course, the actual father of the baby isn't actually around. Simon is somewhat nervous as he helps deliver the baby, but then he says that it's the first time he's done so and handles it about as well as he can.
  - River says that it's her first time too.
Played with on the American version of The Office. Pam is in the late stages of a rare-for-TV normally progressing labor, and wants to hold out on going to the hospital until midnight so their crappy health insurance can't stiff them out of a day's worth of medical care. After spending months going through all the preparations and diapering everything from footballs to cats, Jim is ready to go now and can't understand why everyone in the office isn't helping him convince her.
Subverted on Doctor Who:In the village dreamworld, The Doctor and Rory start freaking out when a pregnant Amy starts screaming and holding her belly. She then reveals that she was faking the Doctor out in retaliation for him calling Leadworth dull.

The Doctor: You're a doctor, help her!
Rory: You're a doctor!
The Doctor: It's okay, we're a doctor. (Puts out a hand to catch the falling baby)

- Also, when Amy thought she was pregnant (turned out it was a false alarm) and decided not to tell her husband Rory, he berated her, saying "I'm a nurse, I'm good with babies," averting this trope. However, when Amy does have a baby when she's been kidnapped, Rory is somewhat emotional, partly because of the shock of suddenly being a parent, partly because his wife had been kidnapped.
In Frasier, when Daphne enters labor in a veterinarian's office, Niles attempts to calm her by getting her to focus on her breathing exercises. Unfortunately, his 'breathing exercises' turn into a hyperventilating panic attack and he faints.
John Ritter memorably played one of these on The Cosby Show.
- Not to mention Elvin when Sondra was about to deliver. She was cool as a cucumber throughout most of the ordeal with the occasional bout of pain. Elvin screeches "Contraction!" when Sondra was in pain and needed to breathe in a paper bag.
Devon (AKA Captain Awesome) in Chuck is way more freaked out by Ellie's pregnancy than she is. The kicker is, both of them are doctors, so he really should know better. When they are finally at the hospital, she calmly tells him to leave the room to collect himself before returning.
One skit from the very first episode of Saturday Night Live was Bee Hospital, with the entire skit being a bunch of worried bee dads buzzing around in the waiting room awaiting the births of their children.
Surprisingly averted in Farscape, when John Crichton is just about as calm as it is possible to be when the love of his life is giving birth in the middle of a battle. He's still terrified, but not nearly to the extreme you'd expect.
The lads on The Young Ones freak out when Vyvyan apparently goes into labor (it's just gas), with Mike fleeing the room and Neil calling for boiling towels and clean water.
Danny, to a point, on CSI: NY. He doesn't get completely out of control, but is still apparently going over things in his head.

Danny: What if it's twins? I mean, you've seen Lindsay, she's huge!

Call the Midwife

Stand Up Comedy

Bill Cosby had a bit in his act about how he panics when his wife gives birth.

Theatre

Mr. Buchanan in Street Scene is under a nervous strain because his wife is about to give birth.
A character in Rogers and Hammerstein's Carousel gets an entire solo about this.

Video Games

Very common in the Distaff Counterpart Harvest Moon games—usually, during the "child born" scene, the Player Character's husband is off worrying. Some of them have only a normal worry, but others are so panicky, they'll get told by the Delivery Guy or gal: "Honestly, I'm more worried about you!"
- Including Alex in Magical Melody and Jin in Tree Of Tranquility/Animal Parade. Both of them are the town doctors.

Web Comics

Deliberately averted with the birth of Mordred in Arthur, King of Time and Space. The News Post below this comic was the Trope Namer.
- And the aversion is taken further with the birth of Galahad.

Western Animation

Fred Flintstone in The Flintstones, during the birth of Pebbles, headed to the hospital without Wilma.
Dexter's dad in the "Laboretto" episodes of Dexter's Laboratory detailing Dexter's birth and development.
Goofy is portrayed as such a father in the Disney short about parenting.
Drawn Together parodied the sitcom cliche of the father running off and leaving the mother behind.
One Hundred and One Dalmatians (both versions) portrays anxious expectant fathers of both the human and canine variety. In the animated version, Roger is acting exactly like this trope, pacing around the room and smoking, when the "children" are actually puppies and Pongo is similarly pacing. In the live action version Roger's waiting on his own child.
My Little Pony Friendship Is Magic shows the end result of this trope in "Baby Cakes". Mr. Cake introduces his twin foals to the Mane Six while sporting a faceful of stubble, an undone bow tie, and his mane and cap in disarray.