Fantastic Romance

For romances that not only involve the use of fantastic plot elements, but are literally impossible to pull off unless one or both parties are chronically defying the laws of physics, traveling through time, reality warping, dimension hopping, or defying culturally accepted norms and standards regarding the mingling of fantastic, non-fantastic, or other fantastic races.

If a character is Trapped in Another World and then gets embroiled in such a romance, they often end up saying I Choose to Stay. If they are forced apart, or decide to return to their own worlds, then they are Star-Crossed Lovers. They may still get a Doppelganger Replacement Love Interest back at home. Such relationships often result in the creation of a Half-Human Hybrid.

Compare Magical Girlfriend and Interspecies Romance.

Anime and Manga

 * Vision of Escaflowne.
 * In Fushigi Yuugi, Miaka and Tamahome.
 * Eureka Seven has this as the driving force between the two leads.
 * In Inuyasha, Inuyasha and Kagome.
 * In RahXephon,
 * To explain further (massive spoilers ahead):
 * The fact that it is heavily influenced by the short story The Dandelion Girl helps explain a lot.
 * In Voices of a Distant Star, the teenaged romantic leads are separated by Faster-Than-Light Travel, so that by the end, the 15-year-old girl's text messages aren't received by her boyfriend until he's 24 and beginning to move on. It is every bit as heartbreaking as it sounds.

Comics

 * In Headstatic, there's a couple who have a Reincarnation Romance like this, who always find each other in every life they live.

Film

 * Avatar
 * Somewhere in Time
 * Time Rider. A man is accidentally sent back in time and falls in love with a woman: he ends up becoming his own great grandfather.
 * Well, at least that means there's gonna be another guy capable of stopping the Flying Brains...
 * The Lake House.
 * Enchanted.
 * The Terminator, where Kyle Reese is sent back in time to protect the mother of future human resistance leader John Connor
 * Stardust
 * The Princess and the Frog, wherein both romantic leads spend the majority of the courtship as magically transformed frogs.
 * Doc and Clara in Back to The Future III.
 * The title character in Don Juan Demarco tells several fantastic tales, all involving gorgeous women, set among beautiful scenery.

Literature

 * The Time Travelers Wife.
 * In Slaughterhouse-Five, Billy Pilgrim engages in such a relationship with Montana Wildhack in a Tralfamadoran zoo. His marriage back on planet Earth is similar, but one-sided. His proper wife just thinks he's gone nuts. And maybe he did.
 * His Dark Materials, where Lyra and Will come from different universes.
 * Twilight: Edward should have died in the flu epidemic, about 100 years ago.
 * : "Day before yesterday I saw a rabbit, and yesterday a deer, and today, you."

Live Action TV

 * The "Time in a Bottle" story arc on Port Charles.
 * "The Girl In The Fireplace" of Doctor Who. Also The Aztecs, and any of the common Classic episodes where the companion stays in the time period because they met someone.
 * The aptly named series 2 episode "Love And Monsters": a perfectly normal man has a relationship with  It Makes Sense in Context.
 * Captain Jack Harkness and  in the Torchwood episode "Captain Jack Harkness".
 * Lost in Austen.
 * Phil of the Future, though not till the end.
 * Pushing Daisies: Chuck should be dead.
 * Primeval has Matt and Emily, both of whom are from different time periods than the show's main one. Matt is from the future, Emily is from the past. They turn into Star-Crossed Lovers when Emily goes back into her own time.

Video Game

 * Saya no Uta: The main heroine, Saya is not a human. And you'll realize how impossible it is for the protagonist to love her under normal circumstances.
 * In Mitsumete Knight, the Asian (the main male protagonist) can have such romances with, and  . Both relationships end up.
 * In Hatoful Boyfriend, even disregarding the whole pigeon thing, the heroine's relationship with  ends with the revelation that.

Web Comics

 * In Sluggy Freelance Torg and Alt-Zoe, as well as Torg and Valerie fit this role, the former being from different dimensions, and the latter from different eras in history.
 * Dreamless
 * Freefall: Florence, a Bowman's Wolf, is technically an AI, while Winston is a genetically-modified human. They aren't supposed to feel attraction for each other.
 * YU+ME: dream
 * Homestuck has a few, but probably the most fantastic and romantic of them all is
 * Slightly Damned hits this one straight on, with the main pairing being the child-like Fire Demon Buwaro and the shy and introverted Water Angel Kieri