Eternal Love

"If you are resolved to drink the bitter poison of cruel eternity, then let’s live on together."

—Shaytan, Seisen no Iberia

"Had we but world enough and time," the poet said to his reluctant Love Interest, "this coyness would be no crime," and he'd be willing to wait for centuries for a Relationship Upgrade. Normal human beings don't have centuries to work out their romantic lives, but the genres of fantasy and science fiction are full of couples who do. Naturally, if you and your beloved are both immortal, or even just really, really long-lived, you may have all the time in the world in which to fall in love, court each other, hook up, break up, and come back together. You might spend centuries in the Will They or Won't They? stage before getting your Happily Ever After, and why not? You have all the time in the world for drama. The result is a Romance Arc which could extend backwards into ancient history or forward into the far future.

Vampires may be especially prone to this trope (when they love other vampires rather than humans), but it can also apply to werewolves, The Fair Folk, gods, artificial humans or robots, and—in some works--magic users whose power grants them exceptionally long lives. Note that any romantic/sexual relationship that lasts for an unnaturally long span of time may count for this trope. It doesn't have to be an entirely happy or healthy relationship.

Tends to be rare in settings where most people are long-lived, as generally the culture has decided that after a couple hundred years even the most passionate of lovers will get sick of one another.

This trope differs from the Mayfly-December Romance in that it only applies to couples where both parties are immortal or near-immortal. Contrast Time Travel Romance and Reincarnation Romance, where the romance arc is extended through time by other means. It may overlap with Living Forever Is Awesome, but if the relationship is a particularly destructive or angst-ridden one, it may fall into the other end of the spectrum.

Examples of Eternal Love include:

Anime and Manga

Mnemosyne has a thousand years-long romance between Rin and Tajimamori, both immortal and eternally young.
Baccano!! has two immortal couples. Firo and Ennis aptly demonstrate this trope by dating for 50 years before finally getting married, while Issac and Miria have been in constant company for about 75 years.
Sailor Moon: Usagi and Mamoru's romance.
In Axis Powers Hetalia, it is inferred that Germany is the Holy Roman Empire, meaning that he and Italy found each other again. Daawww...

Fanfic

In the Suikoden III fic "Eternity, it takes a few centuries for Chris and Hugo to get together.
In the Harry Potter fanfic "Death of Today", a surprisingly sane and horcrux free Voldemort and his soul mate Izar Black are set up to become this. However, this being Voldemort, it involves playing 'games' and messing up societal order in an effort to keep themselves entertained for eternity. Still, Izar fully expects to become sick of living after a millenia of so.

Film

In Hancock, Hancock and Mary have had an off-again-on-again relationship for many centuries. However, this trope is inverted in that the superman/woman pairs lose their powers when they come together so that they are able to grow old together.
The film version of Stardust ended with Tristan becoming a star, and living forever with Yvaine. (In this story, stars are actual, living people, not just mementos of the dead.)

Literature

In the Mercedes Thompson book Silver Borne, Sam and Ariana are given a chance to meet again after centuries and rekindle lost romantic possibilities because of their respective long lives.
Gaston and Freia, from Elizabeth Willey's The Well-Favored Man, are said to have taken decades to fall in love. They can do this because members of their family live for centuries.
Andrew Marvell's poem "To His Coy Mistress" invokes the possibility of a never-ending love affair only to reject it: since the speaker in the poem and the addressee are both mortal, they'd better hook up sooner rather than risk never getting together at all.
The Dresden Files has an Unholy Matrimony example between Nicodemus Archleone and Polonius Lartessa, both made immortal through Demonic Possession over a thousand years ago. Many characters, however, reasonably suspect that their twisted relationship cannot be love in the usual sense.
- Particularly when it's shown that Nicodemus regularly cheats on Lartessa. With their daughter.
The Cullens from Twilight all count, in that they and their vampire mates will simply go on sparkling together forever.
Roger Zelazny's The Graveyard Heart features a couple who achieve their long-lasting relationship through science rather than supernatural forces: they're members of a group that put themselves into cryogenic stasis for years at a time, only coming out of it to throw a huge party, and going back into stasis afterwards.
In Greg Egan's Schild's Ladder, before Tchicaya finally gets to have sex with his childhood lover Mariama he contemplates "Nothing could have lived up to four thousand years of waiting. Except perhaps an original theorem."
Diana Wynne Jones' A Tale of Time City features an immortal or near-immortal couple: Faber John and The Time Lady. They have been separated for thousands of years but that doesn't seem to have broken their love for each other once they're reunited.
This trope applies to all of JRR Tolkien's Elves, since they are immortal and it is stated that they fall in love early and for life. But an outstanding example is Elu Thingol who meets Maia Melian in a forest and then they spend centuries just standing there and looking at each other.
The Secrets of the Immortal Nicholas Flamel has Nicholas and Perenelle Flamel, naturally.
In the closing moments of Greg Bear's The City at The End of Time, it is revealed that Sangmer and his love, who are forced to spend literally eternity apart in order to prevent the end of everything, meet again every time the current universe reaches it's end, only to part again when the next one is created.
The High Elves Caelir and Rhianna in Graham McNeill's Ulthuan Duology. Rhianna must take her ancestor's place on the Isle of the Dead, being trapped there forever, and Caelir, dying from a wound, chooses to stay with her. The two are kept together and will eternally be in a moment of perfect bliss with each other.
Deconstructed by CS Lewis in The Four Loves. It is pointed out that expecting eros to be more then intermittent is unrealistic and besides unfair to your love interest(your emotions are not his/her fault after all), that you should have friendship and affection as well and in any case, if you really want Eternal Love the only way to get it is to submit it to God so he can not only love you but bless your love of other humans.

Live Action TV

Russell and Talbot of True Blood are a good example. Bill's off-again-on-again love/hate relationship with Lorena may fit as well.
From Highlander the Series, you've got the four-hundred year old immortal Duncan MacLeod and his three-hundred-and-fifty year long on-again, off-again snarky romance with the twelve hundred year old immortal Amanda Devereaux.
- There's also a pair of immortal friends of Duncan's who've been married for centuries.
Spike and Drusilla from Buffy the Vampire Slayer were together for at least one hundred years.
- Angel and Darla were together for 150 years.
In The Vampire Diaries Katherine wants this with Stefan. Damon also uses the threat of it against her to convince her to help to delay Klaus' plan until Elena won't become a vampire because of it, by asking her how she feels about competing with Elena for Stefan forever.
The Supernatural episode "What's Wrong with Dr. Phil?" features a pair of witches, Don and Maggie Stark, who have been together for 800 years, despite some rocky times.

Don: You're the woman I want to never grow old with.

Mythology

According to a Greek myth, the wedding night of Zeus and Hera lasted 300 years, and since they both were happy this was the happiest era in the world's history.

Theater

One wonders if some of Oberon and Titania's relationship woes in A Midsummer Night's Dream stem from the fact that they've been together forever and are getting bored.

Video Games

In Planescape: Torment, the relationship between Nameless One and his ghost girlfriend is confusing, but still qualifies.
One of Avernum 3's sidequests involve a vampire who asks your party to deal with a group of ogres who have killed his beloved.
Anogia 's goal is to live with Miria forever, and depend on you he may die, Miria disappeared from this world or he just gave up and spend his time with Miria the rest of time that he has.

Web Comics

Deconstructed in Errant Story, where the long-lived elves consider a near-eternal relationship to be tragic because you'll eventually grow bored with each other. One of their greatest forms of romance is when your partner dies at the height of your love, so you can go on remembering all the good times without having any bad times to deal with. Thanks to their short life spans, humans were considered ideal for this purpose.

Western Animation

Gargoyles' Titania leaves Oberon every so often for a couple of decades to have some fun studying humans' magic called "science," hooking up with human men and even having Half-Human Hybrid children (including Fox), although she always comes back when she gets bored. Oberon doesn't mind; he even finds her latest affair with Reynard highly amusing.

Fox: Mother, who is this guy?
Oberon: "Mother"? ha-ha Titania... what have you been up to?