Ichigo's Hollow form in Chapter 350 is sometimes (incorrectly) called "Vasto Lorde Ichigo". Other names include "Mullet Hollow", "Bull Ichigo", "Demon Ichigo" and "Hell Knight Ichigo".
Also "Super Hollow Ichigo", seeing how his hair grew real long, like Goku when he goes SSJ3.
There is also the rare "Luna Cortante", which is Zangetsu's name in Spanish.
As of Chapter 420 Ichigetsu or Getsugo seem appropriate, or even Ichigod.
Also the Hollow Cow.
His constant upgrading power instead of dying led to Ichigo being called "Holy Lord Ichigo."
Also called Scarmask: named after the chapter where the concept art for his superhollow form was the featured cover.
"Ichithing" seems to be very popular in forums.
Originating on Mangahelpers, the term Ichigonator caught on to refer to the full hollow form beating the hell out of Ulquiorra. Obviously referencing Terminator.
The Pimpcoat - Ichigo's Bankai outfit.
Shirosaki - Ichigo's inner hollow. "Shirosaki" is a play on the black/white symbolism (Kuro means black, Shiro means white), as he looks almost exactly like Ichigo, only in negative. In the English-fandom he's known as Wichigo/Hichigo (white/hollow). There are also alternate fan nicknames for this: Ogihci ('Ichigo' spelled backwards), "Hollowichi", or even "our DLHF" (Dear Little Hollow Friend).
George is the name of the fused Tensa Zangetsu and Super Hollow Ichigo, due to a lack of any other sensical thing working.
Zanbyakuya: Used derisively for Tensa Zangetsu's Inner World form, which bears a striking resemblance to the 6th Division Captain.
Banzooka - Soi Bean's bankai, which is too large and bulky for her to effectively use in combat, but fires one HELL of an attack at range. Said bankai has also been recently referred to as the Stinger Missile due to her bee theme
"The traitor squad" for squad three or Rogue Squadron, because three captains in a row (counting fillers) turned their backs on Soul Society (though the first didn't have a choice).
After becoming Captain Commander due to Yamamoto's death, he has gained another one: "BossRaku"
Captain Shota. Also sometimes called "Captain Jobber", due to the fact that he could never win against truly powerful opponents despite his position, and even against weaker ones he still has to struggle.
Some also call him IceFail, in reference to his zanpakuto's relatively ineffective ice attacks.
Captain Bankai Whore, since he never bothers with his Shikai, every time after his first fight he uses Bankai. Though this is sometimes also used to refer to Ichigo (minus the "Captain" part, for obvious reason). (Both of them tend to go straight to bankai because their shikais kind of suck.)
Ichigo is always in his Shikai now, so he only can go into his Bankai when his level of power proves insufficient to defeat his opponent...
The Christmas Tree - One of his Bankai's special abilities that he uses to freeze Harribel. Guess what it looks like?
Less derogatorily, another good nickname in the vein of Captain Shota is "Captain Kid". Bonus points for being one letter short of Captain Kidd.
Captain Grumpypants, due to his perpetually grumpy mood.
Clown-face is a rather popular one in the fan fiction community.
Captain Consumption (or Captain Tuberculosis) - Ukitake, who coughs quite a bit in his initial appearances. Word of God confirms he has tuberculosis, which is strange, because Ukitake is a ghost.
Technically, he's not. He was born in Seireitei, rather than being the spirit of a person who died... but that of course makes even less sense, since in theory a ghost who died of tuberculosis could 'carry' the disease into death with him, while Ukitake has no excuse.
Now that we know Sogyo no Kotowari's shikai abilities, Captain NO U seems fitting.
Sogy-chan and Koto-chan: The twin spirits of Captain Ukitake's zanpakutou Sogyo no Kotowari. Which one's which is anybody's guess.
Or the "Bad-Eyesight-Trio". Because, you know, one has glasses (and destroys those dramatically), one never opens his eyes and one's blind...
Captain Broken, for having abilities too powerful for an anime character: for instance, stopping the main character's sword attack with one finger. Also known as "Captain Superman/Evil Superman", as a reference to his invincibility and to his Evil Makeover resembling Clark Kent's switch to Superman (minus the suit).
The Other Sasuke - Their first names sound alike and they both betray their people, not to mention being utterly massive Base Breakers.
Aizen's strand of hair that isn't pulled back is known as The Bitchcurl.
His evolved form has picked up a few less-than-respectful ones, such as "Condomman, the Walking Condom, Condom!Aizen, Tube Sock Ninja, Captain Broken Condom", and "Grand Dragon" for his resemblance to a Ku Klux Klan member.
And now that that form was revealed to be a sort of cocoon that he was in while he completed his transformation, his newer form has picked up several new names, including "Butterflaizen" and "Captain Mullet"
As of chapter 415, "Butterflaizen" seems even more appropriate for his newer newer form, as he has grown 6 Narmy butterfly wings.
And now, as of chapter 419, in a new Hollow-like form with questionable openings all over his body - Ladies and gentlemen, I give you: Vagizen. Less NSFW-ish(and as a result, less common), we have Abominaizen
And to get to his Mullet form and Butterflizen form, Aizen is said to have gone through "Gagafication".
The Other Hazama - Named for the now famous Expy of himself who is currently the God of Trolling.* Both characters are voiced by Doug Erholtz in their respective English dubs, albeit Doug only took over temporarily for Erik Davies.
"HAG" (Hot Arrancar Girl) - Before Tier Harribel's name was revealed, she was known to many as this.
Before she transformed the nickname was Underboob.
Or Halle Berry.
Her three Fraccion (Emilou Apacci, Cyan Sung-Sun and Franceska Mila Rose) have recently garnered the name "Tres Bestias," in-universe epithet given by the Hollows to refer to how they served as Harribel's enforcers. Fans have since followed suit in calling them by that title.
Before that happened, though (and after it happened too), these three would be called The Halibabes (from "Halibel", an incorrect romanization of their mistress' name).
The Saddest Clown in the World/Mexico* See below nickname for Hueco Mundo- Ulquiorra Cifer, a stoic Arrancar whose Facial Markings, Perpetual Frown and chalk-white skin make him look like a crying, whiteface clown.
Ulq[Insert Random gibberish here] - because some people don't like trying to spell his name.
Ulqiblahblah - For The Stoic, he sure does talk a lot.
"Emo Clown" is another popular one.
Also, "Emocar" (his facial markings bear a resemblance to emo makeup).
Emospada. Hell, anything with 'emo' in it tends to work.
Alky Whora. Just because.
L-quiorra, because he looks and acts like L from Death Note.
he has a few nicknames, too. The most common one is "Shaq Fu", since he looks like Shaquille "Shaq" O'Neal. Alternatively, there's a variation of "Las Noches" that uses... a different n-word. Three guesses where that nickname came from (hint: it starts with "4" and ends with "chan").
Pumpkincar, because his released form looks like a giant pumpkin with eyes.
The then unnamed Stern Ritters had a few nicknames to distinguish them, like "OMQ" (Old Man Quincy) or Commissioner Gordon for the glasses-wearing one.
Among the named Ritters, we have "As Troll" (As Nodt, due to a certain meme inspired on his Un-Smile after stealing Byakuya's bankai, "Bambi" (Bambietta Basterbine, for obvious reasons), "Quammy" (Driscoll), ether "Punkie" or "Punkdereich" for Bazz-B (the one with a massive mohawk), and "Blondie" for Haschwalth.
Haschwalth also became known as "Lord Toofsy" when 4chan users realized you could use Re-Captcha, an anti-spam tool used on the imageboard, for naming the Stern Ritter - Lord Toofsy was one of the few that stuck.
Quincy Ezio: For Cang Du, the hooded Sternritter who has a scar on his lip and uses a retractable blade as a weapon, much like the aforementioned Assassin.
Quincy Zuko: For when he took the hood off. Revealing himself to be nearly identical to the Fire Nation prince.
Bambietta Basterbine is now known as Miss Psycho Bitch, due to her being incredibly Ax-Crazy. This phrase originated when she sliced a guy in half after seemingly having sex with him.
Her friends Candice Catnipp and Giselle Gewelle are known as "Panty and Stocking". Take a look at them to see why.
Her other friend Meninas McAllon, due to being kind of an Identical Stranger to Orihime, has been called "Evilhime".
"FemRitters" is the designation given to female Sternritter, most especially with regards to Bambietta's crew.
After chapter 569, As Nodt has been dubbed "Marilyn Quincy" because of his REALLY CREEPY Vollständing.
"Stinkmeaner" for Guenael Lee, because he looks kind of like that character from ''The Boondocks".
Papagami, for obvious reasons.
The fan fiction community seems to like calling him goat-chin or goat-face.
From the Shusuke Amagai filler arc:
Big McLargeHuge, Thick McRunfast, Dirk Hardpec, etc. - The silent, tall and muscley bodyguard of the princess in the latest filler arc. All MST3K references.
Fillergami - derisive term for Shinigami created for the filler.
Captain Tuning Fork - Shusuke Amagai, the new filler-only captain, who wields a secondary weapon(a bakkoto). Three guesses what it looks like.
And for the Big Bad, Shusuke Amagai - Amagaizen for being a ripoff of Aizen. Their first names are even similar: Shusuke and Sosuke, as well as another "traitor", Kisuke.
Kamen Rider girl: The vizard Mashiro, because her entire design is an Homage to Kamen Rider.
Zangetsu is now often referred to as Bachgetsu, Juhagetsu or Zan!Bach, due to the revelation in 540. It is because he looks like a younger Yhwach from 1000 years ago.
Namek - Soul Society, to people that view it as a Plot Tumor. In "honor" of the setting of the long, long Frieza arc in Dragon Ball Z. Usage: "Are they still on Namek?"
In the same vein, Hueco Mundo, better known as Mexico. "They still stuck in Mexico?" This lost some of its power when the story shifted to the Fake Karakura arc, although Ichigo and his friends are still inside "Mexico". Both have lost their luster due to the fact that the heroes are no longer in either dimensions in canon.
Karakuri Town - The fake Karakura town that Aizen invaded.
Plotkai - Any new plot power that appears. It's also applied to any Ass Pull on the show plot twist the user is dissatisfied.
Titty Kubo, Kubo Tits, Beaucoup Titties, Kubo Titties, etc - Tite Kubo. One look at Rangiku Matsumoto (or half the women in the cast) should tell you why.
RAEPFACE - Any Off Model and creepy-looking face, especially those made by Ikkaku◊ or Gin.
"THIS IS MY FILLER FACE! -insert goofy narmic face here-
The Bancouch - Aizen's ridiculously large couch.
The Couch Behind The Man
Soul Penis - the Zanpakutou. (Snickers were heard throughout the Soul Society when Ichigo was described as having a zanpakutou as long as he was tall and lacking in impulse control.)
And remember kids, never judge a man by the size of his... sword.
And then there's the manner◊ in which Mayuri carries around his zanpakutou.
Also, the manner of how Pesche pulls out his zanpakutou, Ultima.
De-armed - What Ichigo does to Yammy after the titanic arrancar obliterates Chad.
Also Diss-Armed, as a combination retaliation and insult.
Ichigo's Angels - The opening for seasons 11 and 12, using Shojo S by Scandal, specifically Matsumoto, Orihime, and Rukia. Many have also compared them to Bond girls since the OP is a lot like a typical opening for those movies.
Alternately, the "Hoagie". (Mmm, deli sandwiches of cosmic power...)
Pwning Festival: Aizen single handedly defeating the remaining Captains and Vizards.
Ever since Ichigo and some of his True Companions Chad, Orihime, Urahara, Nel and Pesche took off to Hueco Mundo to fight the Vandereich there, their journey has been renamed as "The Hueco Mundo Road Trip"