New Child Left Behind

An Always Male main character—for obviously biological reasons—gets an Always Female character pregnant, just before leaving to... do whatever. The original version of this is for this to happen during a war movie.

The protagonist has shore leave or something just before shipping out to the war zone, or maybe the war came unexpectedly and he got drafted without warning. He leaves to go off to war leaving behind a pregnant Love Interest. Can be combined with Altar the Speed.

Occasionally even the mother didn't know she was pregnant until after the male leaves, but often the lover left behind will not tell the father because she "didn't want to distract him" or "worry him"—though it's just as common for the father to receive a letter announcing the birth. Usually this letter arrives when the father is in either a prison camp, or in a muddy foxhole while under fire. Something to juxtapose the brutally and ugliness of war with the joy and innocence of a new baby. Expect the father to become stunned and speechless for several minutes, and for his comrades—even the cynical Deadpan Snarker or Drill Sergeant Nasty of the group—to become respectful and moved by the news. A joyful makeshift party might follow. If in a prison camp this has a strong possibility of a Pet the Dog moment for the prison guards.

Sometimes the Love Interest deliberately wanted to get pregnant (this is Lampshaded, and then averted, in Since You Went Away). This was a Truth in Television, and in many places still is. It represents the desire of a woman to have something of her lover to keep in case the worst happens to him. Of course, there is also some Wish Fulfillment for the man as well, since he gets to leave a mark on the world though he's going off into danger. A child means that part of him will live on if he dies.

This war movie trope has then been extended to other settings where the Hero has to leave to go risk his life to save the world- or something else that's dangerous but necessary and suitably heroic. This often captures the emotional aspects of the trope but can lead to Fridge Logic, particularly the further away from the war movie setting you get, as you wonder why the father can't at least show up in between his adventures. It can be handled well, though, given enough justification.

Sometimes it's an unimportant minor character that gets pregnant, and it doesn't have any long-term repercussions whatsoever (for the story and the father that is). He probably doesn't even know she got pregnant; because she's just so considerate she decides not to tell him. In that case, his blissful ignorance neatly evades any and all of the inconvenient Moral Dissonance of being a deadbeat dad.

There has always been some Values Dissonance with the trope, and it has become increasingly so with the shift in values in the West. That doesn't change the trope from being an expression of strong silent desires held by both men and women.

Sometimes the woman's existence is Retconned so that the main character can suddenly have a son, since of course a hero sires a male heir. In this case, see Luke, You Are My Father. Glorified Sperm Donor is another form this can take. If the father dies, this becomes Someone to Remember Him By and may overlap with Her Heart Will Go On.

Examples of New Child Left Behind include:

Anime and Manga

One Piece. Gold Roger got Portugas D. Rogue pregnant with Ace soon before he was captured. Rogue managed to stay pregnant for over a year as to make sure her child would actually be born.
Inverted somewhat in the anime Bokurano when Chizu Honda is found to be pregnant after she has gone off to save the word via giant mech. Her lover, who is also her teacher, ends up being the one left behind and alive. Not that the jerk deserved it.
In Fushigi Yuugi, Hotohori and Houki have been married for about a month, and Hotohori needs to go fight Nakago and his army. Meanwhile, Houki is pregnant with Hotohori's son Boushin. Nakago kills Hotohori, so he never gets to meet his son while he's alive. As a ghost, however, he does.

Comics

X-Men: In the "Fling" story, Colossus was seduced by girls who had the expressed intent of getting pregnant, and he objected on the basis that he couldn't stay to be a father. They told him children were raised by the whole tribe and they really did want his babies because he was obviously good breeding stock. (OK, it wasn't quite that bad.) So the writers went out of their way to avoid the implication of the (young and idealistic) character acting without consideration for the consequences.
At least one of Wildcat's kids is like this.
Teased with the Flash. The one-nighter clearly thought that the kid was Flash's--understandable, since the baby's eyes flashed with lightning. She died before she could tell Flash (and might not have for she respected his current marriage to somebody else). Then it turned it out was actually the Weather Wizard's. Awkward.
At the end of the Superman arc New Krypton, Mon-El gets trapped in the Phantom Zone again, and his girlfriend Billie reveals to her uncle, the superhero Guardian, that she's pregnant right as they're skipping town.
Some Batman stories have this element.
In Elf Quest with that bit about "leaving a kid behind so in case I die, there will still be something of me left." Skot said this shortly before his death. Basically, to the Go-Backs, life was just doing what you could for as long as you could, and then having a kid who could keep going after you. It was described visually as a person walking through the snow, then collapsing, and another person carrying on from that point... a little depressing, but solid enough as a belief.

Film

Superman Returns with Supes and Lois' son.
In that quasi-Groundhog Day movie, Premonition, this happens.
In Pirates of the Caribbean: At World's End, after the final battle and Will and Elizabeth's wedding, the pair spend the day together and he gives her his heart before he sails away as captain of the Flying Dutchman. The movie's Stinger reveals that, ten years later, he returns to find that he has a son.
Lampshaded and then averted in Since You Went Away.
Captain Kirk has this in Star Trek II the Wrath of Khan. Justified when Kirk comments to the mother: "I did what you wanted, I stayed away".
In Sailor of the King Captain Richard Saville and Able Seaman Andrew Brown are in for a shock and Lucinda Brown is going to have some explaining to do.
In the original Yours Mine And Ours the father ships out to sea only to learn that another child will be added to their family, his son Joseph John.
Pear Harbor ends with Rafe holds a dying Danny in his arms, telling him he can't die because he's going to be a father. With his dying words, Danny tells Rafe to raise his child for him. Rafe does raise Danny's son whom they name Danny.
Species is about a hot blonde human-looking alien looking trolling L.A. for a human mate to impregnate her. Several unsuitable candidates who never get to close the deal get killed along the way. Eventually she gets spermed by the science geek. She feels the conception taking place while still straddling the guy, and then kills the babydaddy, too. Minutes later, she gives birth in a sewer.
- Species II plays this theme in the exact opposite way. A male alien goes around planting his seed in every woman that takes his fancy. They all die moments after being impregnated, by the alien baby that litterally explodes out of their belly, leaving creepy Daddy to take care of them in his creepy barn.
  - The end of Species II/start of Species III re-reverses the concept yet again, where the main character knocks up the sexy female alien, before dying in the climactic fight. Though is seems like he kills her after doing her, the final shot of the movie shows her belly expanding to pregnancy-size. This is resolved in the sequel when the mother comes back to life and gives birth to a pure-breed alien baby, before being killed herself.

Literature

James Bond is supposed to have had a son by one of his many conquests (In the new books, not the originals).
Defied in Harry Potter and the Deathly Hallows, after Lupin and Tonks get married and Tonks gets pregnant, Lupin learns that Dumbledore sent Harry on a secret mission and offers to go with him to assist him in whatever he can, Harry refuses and tells him that his wife and son are more important and leaving them would be an act of cowardice. Lupin storms off but realizes that Harry was right and spends the rest of his time with his family.
In Robert A. Heinlein's Time Enough for Love, nearly every single female member of Lazarus Long's forty-third century family sleeps with him in order to get pregnant prior to his departure on a Time Travel trip back to early 1900's Kansas City, Missouri. They feel certain that he is going to "get his ass shot off" in that primitive era, and want Someone to Remember Him By.
Harry Keogh's wife falls pregnant at the end of Necroscope, but he doesn't find out until the sequel (when he's already dead).
A variation on this happened in Myst: The Book of Atrus: Atrus' mother dies giving birth to him, and his father Gehn leaves for the ruins of D'Ni, cursing his mother Anna as he leaves, who ends up raising Atrus in his stead.
Played with in an Apprentice Adept book by Piers Anthony. It has been prophesied that Lady Blue will have "a son by two"—her second husband—so protagonist Stile marries her just before going off to do something dangerous, leaving the marriage (temporarily) unconsummated as a little extra insurance for his survival. It works.
In The Night's Dawn Trilogy, notorious womanizer Joshua Calvert uses a business trip to a planet with self-imposed limits in technological and social progress to seduce and deflower the teenage daughter of his business partner. After he leaves the planet again, she finds out she's pregnant and he finds out he does not forget her as easily as his other affairs. Both are greatly chased around by the plot, so for the majority of the trilogy the trope applies. Fortunately for them said plot seems to wrap up quickly enough that they are reunited even before the pregnancy is immediately recognizable.
A genuine wartime version of this trope occurs in Margery Allingham's Albert Campion series. Campion marries his longtime fiancée just before going overseas for three years of dangerous intelligence work. He is overcome by a strong emotion nine-tenths pure embarrassment when he finally gets home to Amanda, to discover a small, blond person not quite three years old playing in front of his home.
In A Song of Ice and Fire Eddard Stark got his new wife Catelyn pregnant before riding off to fight in Robert's rebellion. When he returned she presented him with his son, and was rather less than pleased to discover that he'd brought another one home with him.
Revan (a sequel to Knights of the Old Republic) has this happen to the titular character and Bastila before he heads off to Sith space, never to be seen again.

Live Action TV

In Stargate SG-1, "A Hundred Days": This may have happened with Jack O'Niell's fiancée when he is Going Native while stranded. It's never proven, but implied from the way she touches her belly when she leaves.
- On the other hand, they still have contact with those people after they leave, so presumably if she were pregnant a plot point about it would come up. Also, it seems a lot like the day he leaves is right after the day he decides to marry her, and she had been talking about wanting a baby, so it could just be her hoping that she is pregnant.
In one Hercules: The Legendary Journeys episode, a reunion of old school heroes visits a training academy and one of the older heroes is casually introduced to his daughter. Of course since the mom was an Amazon, her lack of a father growing up was completely unremarkable and not a source of angst to anyone but him.
Happens in Farscape's season 2 in the "Look at the Princess" episodes. The pregnant mother is stuck for the next 80 years or so in a kind of unaging stasis which Crichton cannot undergo anymore, so at least he's got a (ridiculously) good excuse.
- Also, think of the reason she wanted to marry him in the first place.
- And his leaving allows the mother to marry the man she's really in love with, giving the child a father, as well.
Charmed: After spending half a season fighting against his duties as an Elder, Leo finally decides to leave the sisters to join the Elders after a near death experience that nearly cost him and Piper their lives. Guess who's pregnant at the end of the episode and what the real identity of the Whitelighter that appeared at the end of last season is? Playing true to the trope, instead of using this as a reason to bring Leo back, no matter how easy it would be for him to visit anyway, Piper and even the grown up Chris insist on not getting Leo involved.
This also may or may not have happened in Supernatural. Despite what the mom said her son was Dean incarnate.
Baywatch episodes "Baywatch Down Under (parts 1 and 2)". One of the lifeguards discovers that an Australian woman he married and later separated from had a son without telling him. She withheld the information because she knew that if she had told him, he would have felt obligated to stay with her.
Part of John Casey's backstory in Chuck.

Theater

This is the entire plot of Mamma Mia!.

Western Animation

The Simpsons: Grandpa Simpson has a kid like this with a woman in England.
As does Cotton Hill (though in his case the woman was Japanese) on King of the Hill