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 bad time connecting with her sister so she asked Applejack for advice. AJ suggested to see her and Sweetie Belle's relationship as an "apple pie". Rarity immediately gets it 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 was to turn Rarity to having a ugly dress. Applejack without doubt rescued and comforted her. Rarity is later shown obsessing over a guy named Trenderhoof in the episode, "Simple Ways" but he has interests in Applejack. Rarity tried hard to impress him by even becoming a farmer herself. Applejack saw the wrong in this so she turned herself into a pop star. Rarity later gets jealous and Applejack explains to her why she should never change herself for someone else. In "Trade Ya!", the group separates into three and Rarity decides to go with Applejack. They soon found 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 traded half of her stuff decides to get Rarity that vintage brooch she always wanted. In "Made in Manehattan", Rarity and Applejack were on a mission called by the cutie map to solve a friendship problem in Manehattan. They were trying to help Coco Pommel build her play but time is running out and they haven't had a plan yet. Rarity freaked out and falled down only to have Applejack catch her. She calmed her down and said there is nothing they can't handle. At last, they solved the problem and the two hugged.

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