Bowsario

Bowsario is the slash ship between Mario and Bowser from the Super Mario fandom.

Canon
As shown with Mario and Luigi: Partners in Time and Yoshi's Island, Mario and Bowser's rivalry had existed since their infancy. Baby Bowser finds Mario to be annoying and has even attempted to have Kamek kidnap Mario and Luigi as children. Mario manages to escape, but Luigi is left behind. Thus, this leaves Mario and Yoshi to rescue Luigi. With Mario's fate as a star child and Bowser's heinous acts, they two of them became enemies.

Years later, Bowser would frequently kidnap Princess Peach and terrorize the Mushroom Kingdom. Because of Mario and Peach's close friendship, Mario goes out of his way to rescue the princess from Bowser. With every instance, Mario ends up defeating Bowser and saving Peach. Bowser has come close to stopping Mario, as shown in Paper Mario and Super Mario Odyssey, but Mario always wins in some shape or form. Their rivalry has brought Mario to fame in multiple kingdoms.

While the rivalry they have is fairly strong, the pair has been shown to work together when necessary. Super Paper Mario has the paper version of Bowser as a playable character due to the end of all worlds, however he only joins Mario for Princess Peach's sake. Bowser's Inside Story has Mario and Luigi being inhaled by Bowser due to a mushroom he ate. Unknown to Bowser, the Mario bros decide to help Bowser from inside the koopa's body. After Fawful is defeated, he discovers this and becomes enraged. Mario and Luigi are forced into stopping him. Post-credits shows a heavily-injured Bowser given a cake with Mario, Luigi, Peach, and Bowser on top as a reward for stopping Fawful.

It is also worth noting that, despite their rivalry, Mario will sometimes invite Bowser to sports events. However, Bowser also has a history of forcing himself into these events as well. After the both of them are rejected by Peach in Odyssey, Mario pats Bowser on the back as a form of sympathy.

Fanon
The premise of the ship comes from the concept of Bowser stopping his constant kidnappings and taking a romantic interest in Mario instead. The ship slowly grew throughout the years, but became increasingly popular after the release of Super Mario Odyssey.

There are two potential reasonings behind this: as mentioned before, Mario is shown to have sympathy for Bowser at the end. It is a fairly common trope for love triangles to end with the rivals falling in love instead. This may be the case here. When exclusive amiibo for the game was released, fans noted that the Mario and Bowser amiibo could almost hold each others hands. Some fans have made photos of the two toys depicting the ship.

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Trivia

 * In Super Mario RPG, Mario is required to find all of Peach's wedding items. If he fails, he may achieve an accidental kiss from Bowser
 * If Mario is dressed in Princess Peach's wedding dress in Oddysey, Bowser will compliment Mario. This is contrary to Bowser's thoughts on Mario in his tux