Starhab

Starhab is the ship between Captain Ahab and Mr. Starbuck from Moby-Dick, of debatable canonicity.

Canon
Though it is unknown whether or not they knew each other prior to the voyage of the Pequod, the relationship between Ahab and Starbuck on board the ship is initially very rocky, mostly due to Ahab's obsession with Moby Dick, which Starbuck finds extremely dangerous and unprofessional. Starbuck confronts Ahab multiple times on the subject, which ultimately escalates with Ahab threatening Starbuck at gunpoint, and Starbuck later attempting to assassinate Ahab.

Immediately after threatening Starbuck, Ahab regretted it and admit that Starbuck was a good person and a more professional whaler than he was. It was at around this point that the two began to reconcile and actually start listening to each other instead of fighting constantly or avoiding each other. As of this, they both start becoming rather depressed (or, in Ahab's case, even more depressed) as they realize that neither one of them is capable of compromising with the other, as their interests are in conflict and neither is willing to give up; despite this, they both still make frequent attempts to sway the other.

Ishmael, as the narrator, mentions a sort of deep bond between Ahab and Starbuck (which could be read as platonic, romantic, or really any sort of bond), which is best shown in Chapter 132, in which the two have a deep and highly emotional conversation and gaze meaningfully into each other's eyes, and Ahab states that he would rather gaze into Starbuck's eyes than see God Himself. Starbuck tearfully tries one last time to convince Ahab to give up the chase, but he is unsuccessful--however, Ahab does aknowledge that Moby Dick is in fact very dangerous, and orders Starbuck to stay on board the Pequod when the boats go out to fight the whale, in an ultimately futile attempt to save him.

Fanon
Though Moby-Dick has a very old fandom (as the book was published in 1851), it is unknown at what point in time people started reading the relationship between Ahab and Starbuck as romantic/sexual. Currently, there are many people who argue that Starhab is in fact canon, and more people who argue that while Starbuck did not have romantic feelings for Ahab, Ahab did have romantic feelings for Starbuck; indeed, there is quite a bit of open implication in the book that Ahab may have been gay.

Different Portrayals
As Moby-Dick is classic literature and thus has been adapted many times, differently portrayed versions of Starbuck and Ahab tend to have very different relationships. In some versions, such as the opera, the toxicity of their relationship is played up, while in others, the degree to which Starbuck eventually loved Ahab is played down (such as the 1956 movie). In the upcoming prequel, 40 Years at Sea, their relationship is explicitly stated to be canonically one-sided, on the part of Ahab. In the 2011 TV miniseries, Starbuck directly says that he loves Ahab, though this is often misinterpreted as platonic.

Fan Base
Due to the common types of people who read Moby-Dick, Starhab is not a very popular ship, generally. However, many of the people who genuinely enjoyed reading Moby-Dick and were active in the fandom, it is a very popular ship, and is generally agreed upon as being canon.

There are not really any ships that rival Starhab, however, the most common argument against its canonicity is that both of them are married in canon; Mr. Starbuck has a wife named Mary, and Ahab has an unnamed wife, though neither of them actually appear. However, Starhab shippers frequently argue that while Starbuck does seem to care about Mary, Ahab does not seem to have any attachment to his wife aside from regret over having married her in the first place.

Notable Fanworks

 * The Queen of Rokovoko, currently the only Starhab fanfiction on Ao3