Dry Docking

That is, un-Shipping.

When fans are absolutely opposed to any canonical hookups by a certain character, because they harbor so much Perverse Sexual Lust that they insist on that character being "available" in their fantasies.

May lead to Die For Self-Shipping-type attitudes if there's a perceived chance that the character might hook up.

There is also a trend of pretend killing the Love Interest regardless of whether its an Original Character or Canon character. Here is a good example (look in the reviews of the artwork, not the artwork itself or its summary).

Probably lies behind at least some instances of Self-Insert Fic.

May lead to Fanon Discontinuity. Plenty of room for Troper Tales. Not really related to Dry Docked Ship.

Anime and Manga

 * At least one Love Hina fan was very happy that Keitaro ended up with Naru instead of Motoko.
 * More than one Axis Powers Hetalia fan has admitted to shipping England with other characters so that they can have America all to themselves. Or wanting to be the one to make Russia feel better. Or pretending that Greece and/or Turkey aren't interested in Japan. And since virtually every APH character is the target of Perverse Sexual Lust for a number of fans, these cases are almost certainly not the only ones out there in the fandom.

Comic Books

 * Wonder Woman is poster child for this trope. Every attempt by writers to introduce a Love Interest for her results in backlash from the fanbase.
 * Lora Innes, the creator of The Dreamer, probably left Nathan Hale single precisely because of this.

Film

 * Note that the YKTTW was originally called "Stay Away From Jack Sparrow".

Live-Action TV

 * People of both sexes did not want Ross and Rachel on Friends to be together, so they could have that couple for themselves.
 * X-Files: Why do you think people were so happy that Mulder and Scully held out for so long?
 * The Doctor Who fandom has "Stay away from the Doctor!"
 * Some because they want the Doctor to themselves, but probably more because throughout most of the series' long run the Doctor has been seemingly asexual, and Status Quo Is God.
 * In MacGyver, Nikki Carpenter (Shoo Out the New Guy of the series) was introduced as a possible love interest for Mac. However, the producers soon discovered that female fans did not want Mac to be permanently attached and Nikki was quietly Put on a Bus.
 * Quantum Leap: Sam did not have a wife waiting for him in the event that he ever returned home. No, he didn't!
 * It doesn't help that in the last season he meets a female leaper  and he even has a daughter with a woman when he leapt into her fiance's body while they were making love.
 * Each of the trio from iCarly get this treatment. Nathan Kress especially, although Miranda Cosgrove and Jennette McCurdy get their fair share.
 * This happens in the Supernatural fandom with the fans who aren't Wincesters. This is why Jo had such a backlash in Season 2 and had to be written out.

Video Games

 * This is somewhat inevitable in BioWare fandoms, considering the huge role Romance Sidequests play in their games, and players' often deep attachments to their created characters. Any suggestion that one of the canonical love interests hooks up with someone other than their own PC tends to drive certain people insane. Dragon Age fandom is especially rife with this. Just a mere throwaway mention in a non-canonical Alternate Universe DLC that suggested in that timeline caused an Internet Backdraft from the rabid portion of Alistair fangirls.
 * While it's only prevalent within the hardcore shippers of these Mass Effect pairings, there are people out there who are vehemently opposed to pairing Garrus, Tali, Thane and Liara with anyone else besides Shepard (fitting the trope, as Shepard -male and female- is a vehicle for the player). Garrus and Tali actually do pair up in the third game if both are still available.
 * Similarly in Dragon Age 2, Fenris and Isabela can develop a friends-with-benefits relationship in Act 3, provided that Hawke has shut down both their romances by that point (either by picking the broken heart option or by romancing Merrill/Anders instead). Needless to say, this led to a lot of hate for Isabela from certain crazed Fenris fans.

Western Animation

 * Can happen in the Avatar: The Last Airbender fandom. Generally, Zutara shippers have the reputation (whether or not it's deserved is an argument that can light a forum ablaze almost instantly) of projecting romance onto the character they identify with and the character they want to tap. However, it's also common for people to go one step beyond and declare that "ZUKO/ME IS THE ONLY THING I SHIP!!!"