Warning: Spoilers Off applies to this page. Proceed at your own risk.
Team RWBY
In the series, one of the first things we learn about Ruby is that she likes cookies. It's now a struggle to find a fanfic where Ruby's cookie-love isn't more like a drug addiction. (Word of God says her favorite food is actually strawberries — and so the fandom exaggerated that as well.)
While Ruby does love weapons, several fanworks make her from weapon enthusiast, into a weapon fetishist. Fanworks also tend to make her into a weapon critic/designer, having a habit of both building new weapons and judging ones she sees.
Ruby as a Stepford Smiler and Sad Clown. This comes from the Grief Song "Red Like Roses Part II" that depicts Ruby's pain over Summer's death; it was written early in development and it's unknown whether the song still applies to Ruby's finalized characterization. The events of Volume 3 leading into Volume 4 and more have increased the idea, supported by scenes of her being close to breaking down such as her talk with Oscar in Volume 5. Volume 7 brings this idea up again, and has seemed to confirm many fan theories about Ruby's anguish about Summer. Flat-out confirmed in Volume 9, where Ruby goes so far as to try to erase herself from existence in order to bring forth another person that she thinks will be better than her.
Weiss's song "The Path of Isolation" contains the lyrics "Scars that cover wounds can't hide the self-inflicted pain". It's meant to be metaphorical as confirmed by Casey Lee Williams, but many fans took it literally.
In the show, Weiss openly admits to being distrustful of the faunus and to hating the White Fang, but the full extent of her prejudice is left ambiguous. Fanworks will often assume that Weiss sees faunus as the inferior beings and/or hates them all regardless whether they belong to the White Fang or not. It can be done to make her look worse, to make her argument with Blake feel more serious, or just to throw some dark jokes.
Weiss having a mental illness, usually depression. This comes from her abused backstory, lonely characterization, and the depressed-sounding lyrics of several of her songs.
It's very common to see works giving Weiss A-Cup Angst.
Blake will have her cat-like attributes exaggerated in fanworks, like having Yang play with her using cat toys. Even her canonical cat-like moments are exaggerated further within the fandom, and Chibi got in on the fun.
Blake being a Covert Pervert due to her fondness for romance novels.
Blake is often given PTSD or depression predominantly due to her past relationship with Adam.
Yang tends to be a lot more pottymouthed than depicted in canon. This comes from Yang's songs featuring a lot of cursing, as well as because of her hot-tempered personality.
Fan-works frequently depict Yang as sexually aggressive, promiscuousDude Magnet. This largely comes from the Hard-Drinking Party Girl facade Yang gave off in the "Yellow" trailer. On the flipside, it's also fairly popular to depict her as an Unexpected Virgin with a side of Aggressive Submissive, though this isn't quite as common as the aforementioned inverse.
Hard-Drinking Party Girl Yang is also very commonplace due to her personality and the fact her first trailer took place in a bar. It could also run in the family, though unlike her uncle Qrow it usually isn't depicted as outright alcoholism.
Team JNPR
Nora is often portrayed as being a Cloud Cuckoo Lander and/or Cute and Psycho in fanfics. Her infamous "We'll break his legs!" line with its accompanying crazy grin in particular has turned her into a Memetic Psychopath. It can be debated whether this treatment of Nora is justified; while she is unusually enthusiastic and says a lot of crazy things, she never actually does anything crazy, at least not more so than other characters.
In a case of Never Live It Down, Jaune hitting on Weiss is often presented as a daily occurrence and often done in the worst possible circumstances. This was jossed mid-way through Volume 2, where Jaune gives up on Weiss so she can be with Neptune.
Jaune is slightly clumsy in canon, but it really only comes up at the beginning and only appears twice (when he fumbles his shield and when Pyrrha hits him with a branch). Nevertheless, the fandom latched on to this, and now it's common to portray Jaune as such a massive klutz that he can't even walk down the street without falling over.
Other
Ozpin's love for coffee is in of itself fanon, as according to Word of God, what he has in his mug is hot chocolate. Despite this, most fics tend to depict him as addicted to the stuff, with more humorous depictions having him nickname his coffee brewer as "coffee-chan''.
It's all too common for fics to present Ozpin as so over-the-top incompetent at his job (or too focused on Trolling his students) that Glynda is the only reason the Academy even functions on a daily basis. In particular, the idea of having to do paperwork is common cause for him to jump out his office window.
A darker change for Ozpin is turning his Guile Hero tendencies into making him an outright Manipulative Bastard, such as spying on his students, employing torture on his enemies, and generally being much colder and crueler than his canon self has ever been shown to be, potentially turning him into a Ron the Death Eater.
