Foe Yay Shipping

So there's these two guys, right? And they spend 95% of their time thinking about each other, what the other one's planning or doing, and whenever they converse their dialogue is incredibly emotionally charged. Fortunately, there's a nice family-friendly explanation: they're arch-enemies, right? Right...

This audience reaction trope happens when fans insist that subtextual marks of sexual tension actually mean that the arch-enemies really love each other, and watch the rest of the show with that assumption.

In Shipping Fan Fiction, they might write alternate universe plots that end in Dating Catwoman resolution. If the antagonist's one-sided crush is already canonically admitted, in these Fan Fics, the protagonist might realize that Stalking Is Love, and reciprocate the feelings.

Compare to Belligerent Sexual Tension, where there's actual romantic tension between the characters.

Anime & Manga

 * Pick a Shonen protagonist. Any Shonen protagonist. It's pretty much guaranteed that there will be tons of Slash Fic about him (or less frequently, her) and his (or her) arch-nemesis.

Comic Books

 * Considering the prevalence of Dating Catwoman in Superhero comics, it's unsurprising that the fans like their Foe Yay Shipping so much. Batman/Catwoman, Batman/The Joker and Professor Xavier/Magneto are probably the most famous examples.

Literature

 * Draco Malfoy and Severus Snape from Harry Potter are both frequently shipped with Harry and/or Hermione.
 * Many people in the Twilight Hatedom ship Bella/Tyler's van.

Live-Action TV

 * The already established Superman/LexLuthor ship got a huge fandom boost from the Smallville television series.
 * One of the biggest Once Upon a Time fanbases is dedicated to Swan Queen, A.K.A. the Foe Yay relationship of the Evil Queen, Regina, and the savior, Emma.