In Eureka Seven movie ending, Renton and Eureka became that very symbolic couple after Earth was flooded. Eureka was reborn relying on Renton's survival, memories and dreams, in a way similar to Eve being born from Adam's ribs.
In Megazone 23 Part I, the character Eve is introduced as a mysterious idol and Megazone is revealed to be a City in a Bottle. In Part 2, Eve explains that she has taken it upon herself to hand-pick a worthy remnant who will survive after the superweapon A.D.A.M. destroys the Megazone, and hopefully make it safely by ark to the regenerated Earth where they can begin repopulating it.
Subverted in The Melancholy of Haruhi Suzumiya: After Haruhi starts splitting off another dimension containing (at the moment) only Kyon and herself, Itsuki temporarily appears from the original world and jokes that Kyon and Haruhi could be the new Adam and Eve and populate the world. Kyon is not amused. Itsuki then theorizes that that won't truly be necessary, and that this new world will become more and more populated as Haruhi continues subconsciously creating it.
Berserk has a purely symbolic example which ironically leads to a world changing plot, as in chapter 46, 47 and 48 Guts and Casca consummate their relationship in forest and they both remain naked together laying by a tree, while the Snake Apostle is wrecking stuff in another forest... Does This Remind You of Anything?. It becomes more literal when Guts and Casca's child born out this event is used by Griffith to become corporeal and in turn recreates the world and leading the human race to a new future.
Gall Force: The Gall Force: Eternal StoryOVA focuses around a crew of a space ship consisting of a One-Gender Race named the Solonoids who are racing to claim a new homeworld and the Paranoids, an enemy alien race. One character is absorbed into an alien gelatinous mass and she ends up becoming pregnant via a Face Full Of Alien Wingwong. The cast surgically remove it, thinking it's an infection, and it rapidly grows into an Opposite-Sex Clone. He and one girl end up being the last two survivors by the end, and go on to produce the entire human race.
Subverted in the manga Eden: It's an Endless World!, where, After the End, two teenagers, Ennoia and Hana, think they're the last people alive. They've both been thinking about the inevitable a lot. After a heartfelt discussion on the matter, they decide to stay in "our Eden", but Ennoia decides that they "don't have to live our lives according to mythology. And that means when we have kids, we don't have to name them 'Cain' or 'Abel', either." As it turns out, they aren't the last people alive, but they might as well be; Most of the remaining population, which is already ridiculously minuscule, has The Virus.
This makes up roughly the first third of the sixth volume of Osamu Tezuka's Phoenix manga, Nostalgia. And while the genetic difficulties are addressed, eventually the problem is resolved when the race of aliens capable of taking on any form send a representative on the behalf of the Phoenix. This crossbreeding creates a new species of half human, half moopie.
Seen in the last page of the Narutaru manga, with Shiina's daughter and Kuri's son, playing and havingsex on the beach where the series started. It's unclear as to whether their mothers are still alive.
In the manga Beautiful People by Mitsukazu Mihara, only two people seem to have survived in Japan (and maybe the world) because they accidentally trapped themselves in a bunker for one week while civilization ended. The bomb just killed living beings on the outside without damaging other objects, so they can loot canned food and survive easily for a while. Hopes for them to re-populate the world are... low, as one is a gay man and the other is a lesbian woman... oops.
Completely averted in Dragon Ball where in Dragon Ball Online, you find out that the last survivors of the Saiyan race, Vegeta and Goku, were unable to rebuild the Saiyan life through interbreeding with Earthlings. Saiyans are now extinct.
Played straight, though, in that somehow Good Boo was able to produce an entire race of beings from just himself. And seeing as he was a creature created out of pure magic in the first place, that doesn't seem very unlikely. He probably just split into multiple pieces and let them become separate beings instead of reforming. Specifically, he read one of Mr. Satan's adult books, and through it wanted to experience love. So he ended up creating his wife (the aptly named Booby), and then hit her with a love beam, thus causing her to be impregnated with a child. And apparently over the span of a few centuries, this occurred so much it lead to the creation of an entire race. Majins must have a lot of free time on their hands.
Inverted in Sonic the Hedgehog: The Movie, where Robotnik wants to cause the extinction of humanity, except for himself and Sara, so they can get married, have children, and live out their days on an empty planet. Sara responds by attacking Robotnik.
Yuji and Marlene in Blue Gender eventually find themselves in this role, even though they weren't the last remaining humans on Earth.
In Sukasuka, the protagonist Willem is the last human alive. It was suggested by another character to his Love Interest, Chtholly, that, as a fellow "featureless", she should start training to be Willem's bride so that humanity could flourish again.