Naruko - Naruto's "Sexy Jutsu" form. Is also used in fanworks for a genderbent Naruto or when Naruto has a sister.
Therapy Jutsu - Naruto's ability to make his opponents flash back to their tragic past during a fight, Naruto tells them why they're being stupid, and it changes the course of their whole life. Also sometimes called Jesus-no-jutsu or Talk-no-jutsu and Naruto is sometimes called Ninja Jesus due to this tendency.
Blonde Ninja Jesus. It becomes more apt with the revelations in Chapter 670 where Naruto is revealed to be the reincarnation of the Sage of Six Paths youngest son. The Sage of Six Paths' in-series nickname being "God of Shinobi" and with Naruto being the reincarnation of his son, Naruto now really IS the Jesus of the Ninja World!
Remember the fact that the Sage of the Six Paths created ninshu? This may have been a part the explanation of why Naruto can do what he does.
GARuto following Naruto's taking a level in badass.
NTRuto - Has gained this from the unfortunate amounts of crossover fanfics that have Naruto stealing Canon couples or harems.
Na-bruto: Spanish portmanteau of Naruto and the Spanish word Bruto: Brute or idiot. Used by Latin American fans. He's also named, in a more derogatory way, as Naputo (literally Narufag)
In Spain, he's sometimes nicknamed Raruto, also a portmanteau of Naruto with Raro (Weird).
Both Naruto the character and Naruto the show are often referred to as Nardo (which is sort of how the japanese pronunciation of Naruto sounds) by mocking non-fans and self-deprecating fans.
Dadruto/Narudad: Naruto is a father of two with Hinata in the epilogue.
Also "Boruto's Dad" due to a Crunchyroll tweet gone memetic.
Hotkage: After he becomes the Seventh Hokage as an adult.
Emo-duck - Sasuke, arising from his perceived emo and the resemblance of his hairstyle to a duck's ass.
Saucegay, Gay Sauce - An affectionate (or derogatory) nickname from fangirls who love their Ho Yay.
Other Sasuke nicknames include Sauce-kay, Sa-SOO-kay (coming from the German opening), and Saucecakes.
Sasuke is often dubbed "The Sauce" by die-hard fans and die-hard haters alike.
Yaoi fans who prefer Sasuke as the uke in their pairing of choice sometimes render his name as "Sas-Uke". Very common for haters too.
Satan Shield - Sasuke's version of Susanoo, as his own hate/inner darkness is apparently the reason for its generally demonic appearance (dark aura, huge horns).
Now officially Dr. Snakes, thanks to Itachi's idea.
The Great Snake Escape - The nickname given to a particularly inexplicable example of Plot No Jutsu when Sasuke escaped Deidara's suicide explosion by summoning Manda (a giant snake), controlled it with genjutsu, and then teleported it away with some ability which was not elaborated on or mentioned again. After the explosion had already gone off not ten feet from him.. While out of chakra.
Charasuke or Swagsuke - His playboy alternate-universe counterpart in the Road to Ninjafiller movie, the former used in the Japanese fandomnote Based on "Charai" - flashy, or gaudy.
Papasuke: In the epilogue he fathers a child with Sakura.
Sakura-haters are fond of the moniker "Pink Roach", "Pink Banshee", or just "Pinky".
Even more sophomoric ones might use "Suckura" or "Failkura".
Less insultingly, "Mamakura" after she had a daughter with Sasuke and was later revealed to have raised her alone.
Before his name was revealed, the leader of the Akatsuki was often referred to by fans as Sir Leader.
ToMaTo - the name given to the character whose identity is severely conflicted within the story; is he merely Tobi, Madara, or Obito? This, combined with the guy's actual resemblance to a tomato, led to the affectionate moniker.
In the Spanish fandom, he's named "Bobito", a Spanish diminutive of the word "bobo". (Moron or in context, "Lil' Moron")
The Mask, because he's constantly wearing one, and it's hard to be sure of who's under it. At least this name can't be Jossed.
The events of Chapter 467 have led people to call his master plan Instrumentality.
The place he sends Karin and Sasuke to in that same chapter has also been called "The box dimension" or occasionally "Hueco Mundo".
After Chapter 599, he gained the nickname "Obitobi" in reference to his true identity, Obito Uchiha. Prior to the chapter, fans who theorized it called him "Tobito", which became more popular after the confirmation. They're also sometimes used when someone refers specifically to one version of the character: the young Konoha shinobi (Obito), the masked villain (Tobi), and the unmasked villain (Tobito), given that they all seem like different characters.
After Chapter 637, Juubito and Tentobito because he has the Ten Tails. Also, from Chapter 639 Fat!Juubito.
After Chapter 687, he gained the nickname The Coolest Guy, after Naruto referred to him like that in one translation of the chapter.
Kisame's merger with his sword in Chapter 471 was quickly given the moniker of Kisamehada. Some even call it his Bankai or Resurrecion. As well as a whole slew of nicknames, like Street Shark, Zora Kisame, the Zero Akatsuki (another Bleach reference), and Garchomp.
Aloe Vera - Zetsu, although this nickname was coined by Naruto himself.
Naruto: Yo, Aloe Vera Guy! Where the hell is Sasuke?
Dei-dei is an affectionate nickname bestowed upon Deidara.
Patrick Star: Deidara's giant suicidal explosion in Chapter 362 that looks like a silhouette of Patrick.
Deidara de Pegaso (Pegasus Deidara) in Latin America, because he was voiced by Jesús Barrero, the Mexican voice actor of Pegasus Seiya, albeit it died out when his voice actor passed way due to cancer.
As of chapter 489 ZombiTachi for Itachi (along with the other deceased Akatsuki members) after being resurrected as a zombie by Kabuto's use of Orochimaru's technique.
There's also "Uchihahaha" for Itachi's Not So Stoic moment in chapter 386 and Sasuke's Laughing Mad moment in chapter 483.
Christachi - sacrificed himself to end Kabuto's Edo Tensei, thus "saving the world" in Onoki's words. Also, a scene detailing Deidara's backstory depicted Itachi silhouetted by light in a temple - as if he were a Christlike figure.
Before her name was revealed, Konan was sometimes referred to simply as "Blue", on account of her blue hair.
Orochimaru and Kabuto:
O-chan and K-Fed - for the coldblooded villains Orochimaru and Kabuto.
Pedosnake/Orochipedo - Let's see... creepy-ass grown man fixated on possessing the bodies of fit, attractive young boys... what does that sound like to you?
Oreo or Oreo-cookie - Alternate name for Orochimaru (his name combined with his black hair and white skin).
Brokage for his obsession with his brother or his ethnicity.
Cougarkage - The Fifth Mizukage, after comments mentions that she finds Sasuke and Gaara attractive.
Bitchkage/Trollkage: the Second Mizukage. Before anything was known about him, it was decided that he looked like a bitch. Then, Word of God confirmed his personality was pretty bitchy. Then when he decided to stop bitching, he kept inadvertently trolling the fanbase and the rest of the characters.
Mummykage: The Second Tsuchikage, because he's wrapped with bandages all over his body.
Sassirama or the Sass Queen for the Second Hokage, Tobirama Senju. Since Orochimaru did not suppress his personality this time around, he's become pretty well-known for being The Comically Serious and a true Deadpan Snarker.
Bunny Foo-Foo, The Foxrabbit - The Fanfiction Forum's nickname for the Nine-Tails, due to his long ears (which were probably based on the fennec fox).
Fillain - Derogatory name given to main villains in filler arcs with generic motives. While not Naruto-specific, per se, use of the term was propagated by the Naruto fandom.
Kishi - Masashi Kishimoto (series creator).
Narutard, Dattebayo - The series, as referred to by annoyed non-fans. It is also a mildly pejorative term for Naruto fans, sometime reappropriated by Naruto fans.
Sailor Hinata, for a scene in a filler episode where she practices twirling around over water, nude and silhouetted by moonlight, in a way that resembles a Magical Girl's Transformation Sequence. Hilarious in Hindsight since her English VA now voices Sailor Moon.
Vengeful Orphan Syndrome: Many, many, many characters in Naruto have had one or both their parents killed and become hateful at the world. Thus, any time an unusually reclusive child or outcast appears who has no faith in anyone, they are likely wrecked over a parental murder and Naruto will end up curing them of their angst. Known occurrences include Gaara, Nagato/Pain, Naruto himself at one point, Neji, Inari, Haku (somewhat), Koyuki Kazahana, Temujin, Shion, the Chikara arc kids (5 in total), Ranmaru, Lady Toki, Isaribi (somewhat), Sumaru, Haruna, Tanishi, Motoi, and of course, Sasuke. And that's not even half the full list.
Mads and Hashi for Madara and Hashirama.
Suedara for Madara.
After Chapter 619, Evil Brain Chakra and Magical Hate Chakra for the evil chakra in the brains of the Uchiha.
Shika for Shikamaru.
"Sharrinegan" for the Sharingan-Rinnegan hybrid eyes used by Hagoromo and Sasuke.
Princess Bunny Grandma - Kaguya, the fabled mother of the Sage of Six Paths and thus an ancestor of both the Senju and Uchiha clans; the "bunny" part comes from her having horns that look a bit like rabbit ears.
Shin from Naruto Gaiden: Onion Uchiha and/or Celebi due to his hairstyle strongly resembling an onion, or Celebi's head in particular. The "Uchiha" part comes with him bearing the Sharingan.
Fans of Sarada have taken to calling her "the Uchiha princess" or just "princess."
Asian fans have called Chocho "Happy Polla" due to their similar appearance and perception of their beauty.
"Shi-Shi", the preferred nickname of Kakashi Hatake.
"Infinite Filleryomi" refers to the particularly egregious Jiraiya Ninja Scrolls filler arc, a sort-of "what if" arc showcasing what would happen if certain characters, such as Naruto's parents and the Uchiha clan, didn't die. These fillers took place just before Kaguya was supposed to show up and stretched for over 5 months, and as a result, didn't exactly get positive feedback.
ANBU gets backronymed in Spanish as Abnormales No Buscan Utilidad (Abnormals who doesn't find any utility) for obvious reasons.
"Hanabae" for Hanabi Hyuuga after her appearances in Boruto and Breakout Character status. Is a pun on her name and the word bae.
"Discount Itachi" for Aoba Yamashiro, since despite not being an Uchiha and lacking the Sharingan, they have similar fighting styles (specializing in illusions, crows and illusion crows).