RariJack

Rarijack is a femlash ship between Rarity and Applejack from the My Little Pony: Friendship is Magic fandom.

Canon
Their rivalry relationship is first shown in the episode, "Look Before You Sleep." Twilight invited them to a sleepover because of a huge storm outside and neither of them were close to their homes. They argued right off the bat about things like dirty hooves, girly stuff, etc because their personalities contrast. AJ is a farmer while Rarity is a fashionista. While it's getting late, Twilight suggests them to got to bed and since at that time her house was small, these two had to share a bed. At the end of the episode, they finally tolerated each other but still kept their attitudes towards another. In "Sisterhooves Social", Rarity is having a difficult time connecting with her sister, so she asks Applejack for advice. AJ suggests to see her and Sweetie Belle's relationship as an "apple pie". Rarity immediately understands her analogy and begs Applejack to help in her plan to get her sister back. In "Magic Duel", a returning character named Trixie comes back to Ponyville and challenges Twilight to a magic duel. One of the acts is to conjure an ugly dress onto Rarity. Applejack instantly rescues and comforts her. Rarity is later shown obsessing over a celebrity pony named Trenderhoof in the episode, "Simple Ways", but he has interests in Applejack. Rarity tries hard to impress him by even becoming a farmer herself. Applejack sees the wrong in this, so she turns herself into a fashionista like Rarirty to prove a point to her— that she should never change herself for somebody else. Rarity understands this after she gets jealous and Applejack explains herself to her. In "Trade Ya!", the group separates into three and Rarity decides to go with Applejack. They soon find themselves arguing over what items they should trade their stuff with. Rarity then decides to be "the better friend" and tells Applejack to trade their stuff for what she likes and AJ is shown arguing back the same thing. Finally, Applejack trades half of her stuff when she decides to get Rarity the vintage brooch she  had always wanted. In "Made in Manehattan", Rarity and Applejack are on a mission after being called by the Friendship Map to solve a friendship problem in Manehattan. To find the problem, Rarity sets up a booth to atttract ponies with “friendship problems”. The booth has a drawing of Rarity and Applejack with a heart between them. Later, they are trying to help Coco Pommel build her play, but time is running out and they haven't managed to figure out a plan yet. Rarity freaks out and falls down only to have Applejack catch her. She calms her down and says there is nothing they can't handle. At last, they solve the problem and the two hug.

Fanon
Rarijack is a common ship in the MLP community because of how their personalities clash and their chemistry with each other. Rarity is shown to often make some flirty gestures with Applejack but she does this with just about everypony. They also have the some of the most episodes centered around them. Lauren Faust herself stated that the episodes focused around these two are very enjoyable to write. Rarijack is rivaled by other Applejack and Rarity related ships, but mostly Appledash and Raridash. This has caused many fans to put Rarity, Applejack, and Rainbow Dash in a love triangle with each other.