Not!Lelouch - The Military Adviser in Akito the Exiled named Julius Kingsley looks and sounds exactly like Lelouch with the possibility that Emperor Charles might have modified his memories before he was sent back to Ashford Academy with Rolo before R2.
Uzaku - Derisive nickname, from the Japanese word "uzai", meaning loud or annoying. He's the best-known Scrappy in the fandom, next to Nina.
Hax, Hack0r - For whenever he pulls physics defying moves out of his ass. Such as running sideways along a wall, or...
Spinzaku - For his ability to execute truly fabulous, gravity-defying, and unstoppable spin-kicks. See Hurricane Kick for the whole description. This one has magnificently grown into a Memetic Mutation.
There are a variety of other * zaku nicknames, too, based on specific scenes from the second season, though these are not nearly as popular or justified. These include Drugzaku (after he nearly drugs someone during interrogation) and Runzaku (after he flees from a duel), Nukezaku (after he nukes the Area 11 capital) in R2 18, Laughzaku or Lolzaku (after his Laughing Mad moment while standing in the remains of the capital he nuked), Roofzaku/Spinzaku MK-II / Ceilzaku ( after performing an upgraded version of his spin kick from the ceiling of the emperor's throne room, breaking the spears of the guards ordered to kill Lelouch after he usurps the throne). Oh, and Zerozaku too.
7-11 - After he becomes the Knight of Seven in R2. Not actually used in the show, but the producers allegedly made him number seven for that reference. Japan had been conquered and renamed "Area 11", and that number became a derogatory term for Japanese.
Noodle Jesus - Based off of Jesus Yamato, who some people think he resembles in several ways. The "Noodle" part is because he was designed by CLAMP (see above).
She is commonly refered to as "Nunners," including on TV Tropes itself. It may be her most popular nickname.
Table-kun - The table that was... uh, "molested" by Nina.
Racist-tan - Nina
Table humper or Table-molester: Nina, for above Table-kun incident.
Genocide-tan, The Euphinator, The Massacre Princess - Princess Euphemia following Lelouch accidentally Geassing her into killing the Japanese. The last is actually used in-series. Another popular nickname for Euphemia is Lacus Clonefor obvious reasons.
Mr. Cellphone Spoiler - Jun Fukuyama, Lelouch's voice actor. The nickname comes from the apparent practice of Code Geass staff anonymously sneaking spoilers for upcoming episodes onto 2chan. One such poster made his posts via cell phone; when Fukuyama commented on a radio show that his PC was broken and he could only surf the web via his cell, 2channers made the connection.
Air - Rivalz, whose relevance to the overall plot of the series is next to nonexistant.
Radner - Gino. Radner was a name considered for Rivalz early in the show's production; upon learning this, fans joked that he was a separate character, who was Rivalz' Evil Twin. When Gino appeared with a silly, friendly personality like Rivalz, but actually plot-relevant, fans declared that he was Radner.
Curly/Emperor Curls - Charles zi Britannia, in referring his curly hairstyle, which coincidentally rhymes with his name.
Chuck - Used occasionally by a few viewers.
Emperocket - After R2 episode 21
The Emperor Crusher - Again, R2 episode 21. Before fading to nothingness he launches himself at Lelouch and grabs his throat, but the way it looks seems like he's performing M. Bison's Psycho Crusher. Ironically, Norio Wakamoto also voiced M. Bison. Sometimes it's just referred to as the Psycho Crusher. Pictures were shooped, videos were made.
Also Sayokopter, after her... "particular" exploits as Lelouch's Body Double. See this, as an example.
Orange-kun - Margrave Jeremiah Gottwald. Used in canon before spreading through Memetic Mutation.
As of R2 the "-kun" honoriffic has been dropped.
STORM OF LOYALTY - Self-explanatory.
"Kabeko" or "Carve-tan" - The girl who Lelouch Geassed into carving a wall at Ashford Academy every day.
Code Gay-Ass - A common mispronunciation of the series' name; the correct pronunciation of "Geass" is "gee-ahs." Nowadays, usually invoked for intentional trolling. It's also frequently used in reference to the sheer amount of blatant Ho Yay in many parts of the show.
Also, "Code Geese".
Marianya - Marianne, after the events of R2 episode 20.
Trollo - Take a wild guess.
The other Rolo - V.V, after he's revealed to be Marianne's murderer and having done so out of jealousy. Since V.V gave the geass to Rolo and both are psychotically devoted to their "brothers"...
Lulu Quality - The staff's practice of "playfully" abusing Lelouch throughout the series (see also: Trauma Conga Line). "Playfully" because the writers said that they do like Lelouch and they wanted him to become a better person, as demonstrated by him learning from his mistakes. Unfortunately, a character with such large successes tends to have large failures.
Knight Of Fail - Dorothea Ernst -as well as sometimes Monica Kruczewski- for well.. being obliterated within seconds by Suzaku, despite being a Knights of the Round and among the best warriors of Britannia.
Code Ge-ASS - the show itself, because of the enormous amount of fanservice.