Sparrabeth

Sparrabeth is the het ship between Jack Sparrow and Elizabeth Swann from the Pirates of the Caribbean fandom.

Curse of Black Pearl
When Elizabeth became little headed, fainted, and fell into the Port Royal bay, Jack dived into rescue her. Jack managed to drag her onto the pier and when the guards couldn't help her, Jack ripped off her corset (knowing that she coundn't breath with it on) allowing her to regain conciseness. When Norrington, her father, and many more guards arrive and are about to shoot Jack, Elizabeth tells them that he rescued her and to put their guns down. When Norrington finds out that Jack is a pirate, he calls for Jack's hanging. Elizabeth points out that regardless of Jack's status as a pirate, he saved her life, but Norrington disregards this point. Jack then grabs Elizabeth and points his gun at her head (which is loaded with a single bullet he's saving for Barbossa), and demands his stuff back from Norrington. While Elizabeth is reattaching his belt and all his items, Jack tells her that they are square on him saving her and then pushes her into the soldiers as a detraction that he uses to escape.

After Jack is thrown in prison, Port Royal is sacked by Barbossa and the crew of the Black Pearl, ending with them kidnapping Elizabeth. Will frees Jack on the promise that Jack will help recuse Elizabeth, which Jack agrees to, especially after finding out that Will's last name is Turner.

Jack and Elizabeth are reunited many days later when Barbossa captures Jack's new crew. After Will explains that it's his blood that they need to lift the curse, Barbossa agrees to release Elizabeth, but does so by marooning her and Jack on the same island he left Jack on last time. While on the island, Jack reveals that last time he was here he only escaped by being rescued by rum runners. With no rescue on the way, Jack and Elizabeth make a bonfire and drink and dance and sing into the night. During the night, Jack explains to Elizabeth that to him the Black Pearl represents absolute freedom and when Elizabeth says that being on this island must be terrible for Jack, he says that at lest the company is better. When Jack awakes however, he discovers that Elizabeth has burned the food, the shade, and the rum to create a smoke signal a thousand feet high to signal the royal navy. While Jack is cross at first, he soon discovers that the royal navy did indeed come.

After they manage to convince Norrington and his navy to go after the cursed pirates, Jack, Elizabeth, and Will begin to fight Barbossa. Elizabeth attempts to convince Jack's new crew to help, but they leave with the Pearl. After Will and Elizabeth destroy some of Barbossa's goons, Barbossa points his gun at Elizabeth, but Jack shoots and (thanks to Will breaking the curse) kills him instead. Due the crew leaving with the Pearl, Jack has to go back to Norrington's ship with Will and Elizabeth and she apologizes that they left.

As Jack is about to be hanged at Port Royal, Will begins to rescue him, so Elizabeth creates a distraction by pretending to faint. As Will and Jack are cornered, Elizabeth steps in and side with them, declaring she is in love with Will in the process. As Jack takes this opportunity to escape, he jokingly tells Elizabeth that it wouldn't have worked out between them. As Jack fall into the bay just as Elizabeth did, he is rescued by his crew with the Black Pearl, with them repeating the same justification as Elizabeth. As Jack takes the wheel and plots his next destination, he begins to sing the same sea shanty that he and Elizabeth sang on the island.

Dead Man's Chest
When Elizabeth and Will are arrested by Lord Beckett, they insist that Beckett call Jack by his preferred title of Captain Jack Sparrow.

Fanon
Sparrabeth sailed in the first movie as a result of Jack rescuing Elizabeth and their interactions threw out the movie, but it was more less drown out by Willizabeth (Will X Elizabeth) with the first movie push was pushing more. Its popularity grew to rival Willizabeth after the second movie showed that Jack was in love with Elizabeth and played up the ship tease between the two. The ship's popularity has persisted even after Elizabeth betrayed Jack in the second movie and married Will in the third movie.

The ship has 340 stories on AO3.

Trivia

 * In a deleted scene, Elizabeth is the one who teaches the sea shanty to Jack.