Therapy Jutsu - Naruto's ability to make his oppponents 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!
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.
In Spain, he's sometimes nicknamed Raruto, also a portmanteau of Naruto with Raro (Weird).
Emo-duck - Sasuke, arising from the Fanon emo and the resemblance of his hairstyle to a duck's ass.
Saucegay, Gay Sauce - An affectionate nickname from fangirls who love their Ho Yay. It is often used in a derogatory matter.
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 Ninja" movie, the former used in the Japanese fandomnote Based on "Charai" - flashy, or gaudy.
Some Sakura-haters are fond of the moniker "Pink Roach", "Pink Banshee", or just "Pinky".
Even more sophomoric ones might use "Suckura".
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.
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 nicknames Tobito and Obitobi in reference to his true identity, Obito Uchiha. 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 his backstory was revealed, Lolbito, Obitcho, Bitchbito, etc. were adopted by people who thought he went from competent villain to wangsty brat.
After Chapter 637, Juubito and Tentobito because he has the Ten Tails. Also, from Chapter 639 Fat!Juubito.
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.
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.
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 - 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.
Dan The Ninja: Tsunade's dead boyfriend, named Dan. Because of the laughably un-ninjalike nature of his name (though Dan is actually a fairly common Japanese surname).
Dan Phantom for his revealed ability to astral project himself.
Sharinnegan: The 10-Tailed Beast's massive eye, which is a combination of rinnegan and Sharingan.
Romeo & Juliet: Ninja version. referring to the Ho Yay relationship of Hashirama and Madara, who were barred from seeing each other due to clan conflicts.
TNJ- Talk No Jutsu: A very knee-jerk term coined by the fanbase used to indicate that a villain has been talked to death via a lecture from Naruto or otherwise. Similarly, Plot No Jutsu, as in a totally out of left field Ass Pull a la Kishi just makes up New Powers as the Plot Demands.
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. CONSTANTLY. Bottom line- exhausted plot point. 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.