A fan Prefered Couple is a TV Tropes term which is basically fanshipping. it refers to two people in media that fans want to become a couple but it doesn't happen usually because it isn't the official couple. This is also the only page in the entire wikia that will welcome fanshipping.
Famous Examples of Fan Prefered Couples
Katara/Zuko from Avatar: The Last Airbender: This pairing is actually so popular it was even referenced in the episode "The Ember Island Players."
Robin/Raven from the Teen Titans Animated Series: On fanfiction.net, there are thousands of stories that get these two heroines together. Also Beast Boy/Raven however, even though they don't get together in the series, they were a couple in several comics.
Ben/Gwen from the Ben 10 franchise: Despite it being incest, this is actually a very popular pairing.
Jenny/Brad from My Life as A Teenage Robot: It was confirmed if the show had continued, Jenny would have gotten together with Sheldon, even though many prefered her with Brad.
Tommy/Kimberly from Mighty Morphin' Power Rangers: Though they were an official couple, when Kimberly left and had Kat replace her, she broke up with Tommy with a letter. Then they show a future where Tommy marries Kat. A LOT of fans were outraged.
Penny/Sheldon from The Big Bang Theory: Despite the fact this will never happen, many fans saw opportunity of this pairing to happen when Penny and Leonard break up in the third season.
Sora/Riku from Kingdom Hearts: Though Sora is in love with Kairi and vice-versa, many like to see Sora with his best friend, Riku.
Sakura/Sasuke from the Naruto franchise: Despite his betrayal and the fact he tried to kill her, this fan pairing remains popular with tons of AMVs, fanart, and fanfiction. Upon the end of the series, this pairing became canon.
Thrall/Jaina from the Warcraft franchise: Ever since the Burning Legion's invasion of Hyjal was thwarted, Jainna and Thrall became good friends to the point where fans thought the two would get together. However, their hopes were dashed when Thrall fell in love with Aggra in the Cataclysm expansion of World of Warcraft. Blizzard is aware of the fan pairing and when you grab a White Punch Card in Dun Morogh, it says in binary, "Thrall and Jaina sitting in a tree. K-I-S-S-I-N-G" as a joke.
Stiles/Lydia from Teen Wolf: Stydia is one of the most shipped couples in the Teen Wolf fandom despite never actually dating, they have shared multiple kisses. Stiles was dating another girl, Malia, and all of the Stydia fans were very angry with Stiles and Lydia not dating yet. Creator of the show, Jeff Davis, says that Stiles and Lydia will be what the sixth season of the show will be revolved around making fans very, very happy.
Lucy/Lincoln in The Loud House. Despite the fact that he's an ordinary human and she is not, he happens to love her and wants her to be herself, which I believe is an important thing in a relationship. Also, in the episode "Back In Black" Lincoln seemed against the idea of Lucy being in love with Rocky, hinting that Lincoln himself secretly loves Lucy.
Patrick/Sandy in SpongeBob SquarePants. They seem to annoy each other to the heavens above, but she sees him as a close friend and, honestly, they laugh together (no metaphor there) and she even gave him a giant chocolate balloon in "Valentine's Day". If she gives him that, she must have feelings for her.
Lana/Surly in The Nut Job. When Precious the pug was staring at Surly, Lana turns around and gives Surly a sympathetic look, and unlocks the cage. Later in the movie, Precious tells Surly Lana is the new Nut Shop owner, probably saying she's allowing him back.
DJ/Katie from Total Drama Island: Before the first challenge, DJ tried to tell her the challenge couldn't be too bad. But how wrong he was and it would only get worse from there.
Brick/Anne Maria from Total Drama: Revenge of the Island: When Jo called Brick dead weight, Anne Maria got disgusted with her and said that while he isn't much to look at, he's still a person.
Tyranno Kenzan/Rei Saotome (Tyranno Hassleberry/Blair Flannigan in English dub) from Yu-Gi-Oh! GX: The two were partners in a tag duel against Judaii Yuki and Asuka Tenjoin (Jaden Yuki and Alexis Rhodes in English dub). I also saw a fanfiction story with the two and got hooked.
Brian/Stewie from Family Guy: Stewie has often times tried to seduce Brian and most of the time I wanted him to succeed.
Kiba/Hinata from the Naruto franchise: He has shown a protective attitude towards her when she was a part of his team.
Wrathion/Any Mortal in the Warcraft franchise: Wrathion is the only black dragon not corrupted by the Old Gods and unlike his father, DeathWing, Wrathion holds a deep respect for mortals, thus it should make sense for him to marry a member of the mortal races, whether it's a member of the Horde or Alliance.