When you travel through time and space, you're bound to run into yourself occasionally. These meetings can be awkward, embarrassing, or lead to uncontrollable fainting, but there are some things your future self can teach you better than anyone else.
The Time Traveler's Wife by Audrey Niffenegger: Involuntary time travel comes with plenty of disadvantages, not the least of which is finding yourself suddenly and unexpectedly naked without any money. Fortunately, the predestination paradox can be a handy survival tool. Time traveler Henry often finds himself sent to the same points in time and space as his younger self, and teaches him how to find clothing, pick locks, and steal wallets. It's sort of like illicit father-son bonding, just with himself.
The Joy of Sex
The Time Traveler's Wife: Another unexpected side effect of time travel is that a horny, adolescent Henry is every now and then confronted with a nearly equally young, equally horny duplicate of himself. This makes for some rather spectacular instances of masturbation, but it's really awkward when his father walks in on him.
—All You Zombies— by Robert Heinlein: The Unmarried Mother was an intersex, though apparently female, teenager who was seduced by a mysterious older man. Many years and a sex change later, she, now he, is sent back in time, where he meets and makes love to a very familiar girl.
The Man Who Folded Himself by David Gerrold: Daniel Eakins is the sort of time traveler who throws caution to the wind, sampling all that time travel has to offer: foiling assassinations, visiting great moments in history, and using his knowledge of the future to bet on the ponies. So it's no wonder that when he meets up with the same- and opposite-sex versions of himself, he tends to get it on with them.
Futurama: Bender's Big Score: When the alien nudists get a hold of the time travel code tattooed on Fry's rear end, they're mostly interested in stealing artifacts from 20th Century Earth, although they do at one point take a time out for Nudar-on-Nudar nookie.
How to Win a Fight
The Kid: Russel Dritz's dirtbag ways may go back to his childhood, when he was picked on by bullies and lost his mother to illness. When Rusty, his younger self, ambles into Russel's life, he finds there are some subtle ways that he can change the past. First on the agenda: Getting the kid into a boxing ring so he can learn how to throw a punch.
How to Become Rich and Powerful
Back to the Future, Part II: The 2015 version of Biff decides that all of his troubles would be solved his he had been extremely wealthy in the past. So he steals Doc Brown's time-traveling DeLorean and, with a 2015 sports almanac in hand, travels to 1955, when he gives the almanac to his younger self. And it seems to work: Biff is rich beyond his wildest dreams, he's quietly had his rival George McFly murdered, and he's married to George's now artificially-endowed widow Lorraine. Of course, it all goes to hell when that pesky Marty McFly appears on the scene.
Gargoyles "Vows:" In move that revealed the entire series as one big predestination paradox, David Xanatos travels back in time on his wedding day to give his younger self a collection of priceless gold coins, along with instructions on how to invest the proceeds from their sale. Is it cheating? Probably, but in Xanatos's mind, it makes him the very definition of a self-made man.
By His Bootstraps by Robert Heinlein: When Bob is pulled thirty thousand years into the future by a slightly older, though no wiser version of himself, he discovers that humans have become a primitive, compliant people. Diktor, a fellow native of the 20th Century, explains that a technologically advanced person could easily become king of these sheep-like folks, and gives Bob a list of 20th Century items to bring to the future. Bob complies, but travels to a point ten years before he meets Diktor. It takes Bob a shockingly long time to realize that he's in a Heinlein story and that he is himself Diktor.
How to Win the Girl of Your Dreams
Futurama: Bender's Big Score: Fry is distraught when Leela, the love of his life, is won over by an older and more mature stranger named Lars. When Lars is revealed to be Fry's older (and this time wiser) duplicate, Fry should probably recognize that he could woo Leela if only he'd successfully reign in his adolescent nature. But it being Fry, he fails to take the lesson to heart, and quickly moves on to another girl.
How to Travel Through Time
The Time Ships by Stephen Baxter: In Baxter's sequel to H.G. Wells The Time Machine, we learn that the Time Traveller didn't build his device completely unaided. A mysterious benefactor gave the Traveller a sample of a radioactive substance to study, a substance that ultimately makes time travel possible. Of course, like all mysterious strangers in time travel stories, the Time Traveller's benefactor is, in fact, an older version of himself.
How to Save the World
Heroes "Five Years Gone:" One of the great things about the power to travel through time is that if you get that whole "save the world" business wrong the first time, you can just keep trying. And Hiro Nakamura has the added benefit of traveling through time to change events himself, and leaving instructions for his much less bad-ass past self.
Doctor Who "Time Crash:" The Doctor meets up with himself a great deal, if for no other reason than two or three or five Doctors are better than one. But sometimes it's just to ensure a little predestination paradox magic. The Fifth Doctor watches the Tenth Doctor create an artificial supernova that cancels out a giant hole in fabric of reality. Naturally, the Tenth Doctor only knows how to do this because he watched himself do it when he was the Fifth Doctor.
Doctor Who "The Parting of the Ways:" Rose Tyler gets her own predestination paradox going when she looks into the heart of the TARDIS. The TARDIS gives her the power to transcend time and space, letting her leave the message "Bad Wolf" to herself in the past that ultimately lead Rose and the Doctor back to this time and place.
Teen Titans "Titans Tomorrow:" When the Teen Titans travel to the future, they're eager to see what they're like as adult superheroes. But the future is unexpectedly bleak, with many of the Titans turned to violence and destruction, tearing the United States in two and turning the Western half into a police state. Fortunately, the Titans are able to learn from their future selves what set these events in motion, and are able to prevent their dystopic future.
Babylon 5: To add another wrinkle in the predestination paradox, Jeffrey Sinclair finds that his entire life is being guided by his future self from the past. Sinclair eventually learns that he is the great Minbari historical figure Valen, and Sinclair must eventually travel back in time, become Valen, and write the prophesies that will guide Sinclair's life in the future. Fate, or proof that his talents transcend time and space?