The most frustrating, annoying thing about the opposite sex is that they're not you. Why can't you just meet your exact duplicate — except for sex? You'd be a perfect match. Luckily, science fiction suggests 3 ways it could happen.
This has been the dream of science-fiction fans and science-fiction authors since the days of "Clone Of My Own" (which is usually attributed to Isaac Asimov, but who knows if it's actually by him?) "Clone Of My Own" goes:
Oh, give me a clone
Of my own flesh and bone
With its Y chromosome changed to X.
And after it's grown,
Then my own little clone
Will be of the opposite sex.
Clone, clone of my own,
With its Y chromosome changed to X.
And when I'm alone
With my own little clone
We will both think of nothing but sex.
There are about 29 versus more, but you get the idea. Actually, after reading authors like John Varley and Ursula K. Le Guin, the whole idea of the "opposite" sex has been thrown into question — surely, once we can all reconfigure our bodies at will, eventually we'll have some sort of sex tesseract.
But for now, here are the ways that science fiction offers, for us to meet our opposite-sex duplicates (and in some cases, have sex with them):
House Of Suns by Alastair Reynolds:
Abigail Gentian, a wealthy woman, decides to explore the vastness of the stars — she she has herself cloned a number of times, and some of the clones are male while others are female. They all share Abigail's memories, and Abigail herself joins them without knowing which of them is the "real" her. And these "shatterlings" have sex — a lot. Especially in the novella Thousandth Night, there are tons of orgies in which all of the clones get together, making it a certainty that the "real" Abigail has been with her clones.
Time Enough For Love by Robert A. Heinlein:
Lazarus Long is the world's oldest human, and he decides not to undergo rejuvenation therapy, thus sentencing himself to death. His descendants convince him to keep on living, but he'll only do it if he gets to have a new experience — so two of his descendants become impregnated with opposite-sex clones of Lazarus. And after the opposite-sex clones of Lazarus are born, Lazarus raises them as his own daughters... and then has sex with them, of course.
"Nine Lives" by Ursula K. Le Guin:
This Nebula-nominated novelette, first published in Playboy, features a set of clones of a man named John Chow who died in a car accident, and some of them are female:
"All chips off the old block," Martin said valiantly. "But how can . . . some of you be women . . .?"
Beth took over: "It's easy to program half the clonal mass back to the female. Just delete the male gene from half the cells and they revert to the basic, that is, the female. It's trickier to go the other way, have to hook in artificial Y chromosomes. So they mostly clone from males, since clones function best bisexually."
Sadly, nine out of ten clones are killed, forcing the remaining clone to deal with unaccustomed solitude.
The Ophiuchi Hotline by John Varley:
The character Tweed has clones who are male and female clones of the same individual, called Vaffa or sometimes Hygeia. They're super-strong, super-big and lethal.
NYX and various other X-Men comics:
X-23, a female clone of Wolverine, first appeared in the X-Men: Evolution animated series, but then made the leap to comics, just like Harley Quinn. Despite looking kind of silly, she's manage to stick around long enough to get her own miniseries and have her backstory explained. I don't think she and Logan ever hooked up, but they have fought, which is almost the same thing when you come down to it.
The Hitchhiker's Guide To The Galaxy:
As Zaphod Beeblebrox explains, the girl Lintilla "has now been cloned over five-hundred-and-seventy-eight-thousand-million times - and has thus created a problem in some quarters." All of the Lintilla clones are female — but the anti-clones, sent to get rid of the infestation of female clones, are male versions of Lintilla called Allitnil. When a Lintilla and an Allitnil come together, he gets the Lintilla to "agree to cease to be" — but Arthur Dent takes a liking to one of the Lintillas, and kills her particular Allitnil.
Hunted by James Alan Gardner:
Edward York is an illegal clone of one of the Admirals on the High Council, and due to genetic problems he's a bit stupid. But a female clone of the Admiral, named Samantha, turns out super-smart and resourceful. Together, Edward and Samantha travel, as brother and sister, travel to the planet Troyen to try and negotiate a peace between two alien species, the Mandasars and the Fasskisters.
Kyle and his fellow vat-baby Jessi aren't strictly speaking clones, because I think they had different genetic stock — as far as I can remember, Kyle came from Adam and Jessi came from Sarah. But they do come from the same vat, and they resulted from the same super-baby program. So they could be considered akin to clones, sort of. Worth mentioning, anyway.
Ultimate Spider-Man: Ultimate Clone Saga:
Can't believe I forgot this one, since I have the trades at home. In the Ultimate version of the Clone Saga, they clone Peter Parker several times... including a female version called Jessica Drew. And Jessica has all of Peter's memories — S.H.I.E.L.D. wants to erase Jessica's memories and set her up with a new identity, but she escapes and takes on the identity of Spider-Woman. Thanks, kwschuttler!
2) Alternate universes
Parallellities by Alan Dean Foster:
Max, the main character of this novel travels through the multiverse, and finally meets an alternate female version of himself — and has sex with her. Later, he manages to find an entire planet populated by copies of himself. As the back cover copy explains:
Now Max was lost in a virtual sea of collateral worlds, confronting man-eating aliens, dinosaurs, talking frogs, dead Maxes, girl Maxes, old Maxes, even ghost Maxes. His only chance to escape the space-time continuum was to find Boles and hope the loony genius could rescue him. But how could he be sure which world was real, which Max was Max, and which Boles was the Boles who could stop the madness—or trap Max in the wrong world forever. . . ?
Red Dwarf, "Parallel Universe":
Our gang finds a device that's supposed to transport them home to Earth instantly — but instead it zaps them into an alternate universe. There, they meet alternate versions of themselves, including female versions of Lister and Rimmer (and Cat's counterpart is a Dog.) Rimmer has to fight off his female counterpart's sexual advances, while Lister actually does wind up in bed with his female version, Deb. And because in this alternate universe, it's the men who get pregnant, Lister winds up carrying his alternate self's baby.
Thanks to Xicer for pointing out this one: in the episode "Double Cross," Quinn meets an evil female duplicate of himself from (of course) another universe, and almost makes out with her:
Transition by Iain Banks:
This dimension-jumping novel mentions that it's quite common to enter the body of your alternate-universe self and find that the alternate self is the opposite sex. This is a known syndrome, which causes some discomfort or confusion among the universe-hoppers whom it happens to.
3) Time travel
"All You Zombies" by Robert A. Heinlein:
This story features a young man who's tricked into impregnating his younger, female self — because it turns out he had a futuristic sex change at some point, which the reader doesn't realize at first. And then it turns out that he's actually the child of that union, meaning that he's his own mother and father — the mother of all time paradoxes, in other words.
The Man Who Folded Himself by David Gerrold:
Daniel Eakins travels backwards and forwards in time many times, meeting himself and having sex with himself — over and over and over. But after a ton of trips, he actually meets an alternate-universe version of himself who was born female, and they shack up together at the beginning of time. It goes great for a while, until they get fed up with each other, and then Daniel's time-traveling female counterpart manages to erase herself completely from Daniel's timeline, so Daniel can never find her again.
Needless to say, this post would not have been nearly as fascinating without TVTropes.org, the fountain of all greatness. Additional reporting by Josh C. Snyder.