Although Yu-Gi-Oh! may not leap out to the casual viewers as a franchise that engenders a strong fandom response, in actuality the Yu-Gi-Oh! fandom has been around for years. All that time, and many series characters, have led to the development of a multitude of fandom ships, some more or less grounded in the canon given to fans.
While Yu-Gi-Oh! doesn't focus too much on the romances within it, the world of fanfic loves a good ship. Here are some fans wish were real.
Yami Yugi/Seto Kaiba
Truly, this relationship is a through-line that the anime will revisit again and again. Yami's initial defeat of Kaiba quite literally changes his life, freeing him from a deep darkness that clouded his mind for years. Though Kaiba never becomes a warm, fuzzy character, he does grow a grudging respect for Yami and never lets go of the obsession of beating him in a duel. Kaiba sees Yami as the only person worthy of his time and attention and devotes huge efforts to dueling him whenever possible, so it's clear where fans see the romance brewing. And, although it is often in the name of something else, Kaiba makes the most emotional concessions for anyone except Mokuba for Yami, sometimes saving, or even sacrificing himself for, him.
The summary of the latest Yu-Gi-Oh! movie, Dark Side of Dimensions, may as well read, "Years after Yami crosses into the afterlife, Kaiba still can't move on."--a fanfiction narrative at its finest. At the end of the film, Kaiba is intimated to spiritually die, so they can be together. It's a passionate affair of the heart, even if not overtly titled a courtship, and would be a great true romance.
Seto Kaiba/Joey Wheeler
Kaiba and Joey have a very traditional rivalry between them in Yu-Gi-Oh's canon, each of them trading constant barbs and insults, and finding the other to purportedly be abhorrent, yet being unable to resist engaging in a fight together. Kaiba often calls Joey a "puppy dog," indicating he finds him to be just a pet to Yugi, and more sniveling and weak than anything else, but fans see how the nickname could quickly turn endearing and have christened the ship, "Puppyshipping." (Joey, meanwhile, favors 'Moneybags.')
While Kaiba and Joey feel they have nothing in common, each seeing the other as their polar opposite, fans revel in the blend of contrast they create; stoic and outspoken, icy and hot. And from an outside view, the audience knows, indeed, that there is much common ground the two share, both having been, at one time, poor children from broken homes, abandoned by those who should care about them the most, and consequently devoted to their younger siblings. If only a singular conversation could happen without insults, these two could make a great match.
Mai Valentine/Téa Gardner
Although Mai and Joey are a canon ship that fans also love, there is a spark between Mai and Téa that captures their imaginations. Mai really seems to dislike men, having had many bad experiences with them over time, but meanwhile, she has a soft spot for women, which especially comes out in her interactions with Téa, both through overt kindness and a more roundabout desire to help her grow.
This lowering of her guard could be a great in-road to the start of the relationship, and where Mai strives to maintain a stony exterior, Téa comes walls down and ready to be open and honest in her feelings. Fans feel they bring to one another elements they don't themselves naturally have and could have a wonderful relationship.
Seto Kaiba/Kisara
The love Kaiba shares with his Blue Eyes White Dragons is probably the most canon ship there is. But, fans of the series know, this romance could be taken a step further, because the spirit of the dragons is actually a woman named Kisara, who is sacrificed for the power of her spirit and whose soul is embedded in the card itself.
While Kisara is a character who lives among the ancient Egypt set, Yu-Gi-Oh! is a show full of reincarnations, spirits, and more. Fans feel if there was ever a romantic match for Kaiba, it would be Kisara and wish that the relationship could be further explored.
Yami Malik/Yami Bakura
Even evil needs true love! Aptly named, Psychoshipping, this romantic relationship could spell trouble for Yu-Gi-Oh!'s heroes but is a lot of fun for fans to imagine. Yami Malik and Yami Bakura canonically team up to cause trouble during the show's Battle City Arc and seem to really enjoy one another's evil way of thinking. In true, Yu-Gi-Oh! fashion they both have incredibly dark origins as well, and so could relate to each other on that level.
Fans enjoy a world where the darker halves of the characters, find a way to settle with their lighter sides, and in that sort of reality, this duo would cause more mischief than madness, merrily holding hands as they run away from their latest scheme.
Seto Kaiba/Serenity Wheeler
Kaiba/Serenity is the Ginny/Malfoy of the Yu-Gi-Oh! world, carrying with them a bit of Romeo and Juliet in a way that endears fans. Joey, Serenity's brother, of course, hates Kaiba, unless he really protests too much, so there would be a natural tension that is fun to explore. While Serenity and Kaiba never really interact, and Serenity seems to have more possible romance with either Duke or Tristan, fans enjoy her warm sweetness and think it would work as a complement to Kaiba's rigid ways.
In true fanfic form, canon doesn't really have to play into the equation for fans to wish a ship would really happen.
Yugi Mutou/Téa Gardner
Yugi and Téa are probably the most intimated ship in the show that did not make it to being canon. Although Téa also shows interest in Yugi's darker half, Yami, it is Yugi who is the true protagonist in the story, and arguably, Téa is his closest and truest friend. There's a sweetness to the possibility in their friendship which isn't truly explored in the show but appeals to fans.
Ultimately, fans feel it would be nice to see two such good-hearted, kind souls find love in one another.
Seto Kaiba/Ishizu Ishtar
Kaiba and Ishizu plot together early in the Battle City arc, and she seems to be a match for him, unruffled by his dramatics and barbs. Ishizu stands her ground calmly and radiates authority in a way that might intrigue and impress Kaiba if he were not so distracted by the idea of the cards and power she offers him.
By the same token, Ishizu is largely manipulating Kaiba, at least, from her perspective, so she might appreciate Kaiba's own selfish streaks and be able to handle them in a way that few others could. They would absolutely be a power couple.
Rex Raptor/Weevil Underwood
Rex and Weevil are a sort of gruesome twosome of their own variety. While they're not shown too much in the series, they make up an echelon of unsavory, minor villains that paints them with the same brush. They both love a theme and have a clear rivalry that plays out largely off-screen.
If there were ever two duellists that deserved one another, it's Rex and Weevil.
Duke Devlin/Tristan Taylor
Duke and Tristan clash endlessly over a mostly hopeless quest to win Serenity's love, but in true rivalry, there is always a seed of potential in something more, especially since Serenity never seems to incline herself to one or the other of them. Famously, they're also seen in bed together in canon, and isn't the simplest explanation always the best one?
The tension between Duke and Tristan is ripe to take that last step into romance.