As expected from show made by former Studio Gainax staff, Kill la Kill is absolutely overflowing with shout outs. The list below is in fact only a portion of all the known shout outs and references in the show. A more complete list is currently being compiled by the fans here.
One that's worth mentioning is the Catch Phrasenote "Let me give you two pieces of information."of Tsumugu note Katsuyuki Konishi, played Kamina in TTGL. , this line was originally Viral's note Nobuyuki Hiyama, who plays Sanageyama in story. line when he first encountered Kamina. So this is technically an ironic line swap.
When Nui rips up Sanageyama's uniform, she calls him a "naked ape." Not only is this Just for Pun, but the fact that this was what Viral, who's a beastman, called human beings in general to disdain them. Now that his actor is playing a human being, this phrase was used back at him as payback.
Most of the main characters including the Ryuko, Mako, Satsuki, Mikisugi-sensei and the student council can be considered to be expy's of characters from Cutey Honey and Re: Cutey Honey. See here.
Ryuko = Cutey Honey - Father killed by mysterious party. Seeks revenge using secret technology created by her father to transform into a scantily-clad warrior of justice.
Mikisugi-sensei = Seiji Hayami - Mysterious man with a connection to the protagonist and her father. Helps her discover her powers.
Mako = Honey Kisaragi - Genki Airhead that only desires friendship and food. Tends to get into risqué situations.
Mako also strongly resembles manga Natsuko - Cute, bubbly Damsel in Distress who immediately decides the new transfer student is her new best friend (and crush).
Mataro = Junpei - Perverted younger brother that has a crush on the protagonist and acts as comic relief
Satsuki = Natsuko Aki - No nonsense woman who doesn't have time to deal with the protagonist's issues. Not really sure if she's a friend of foe?
Shitennou = Gold, Cobalt, Scarlet and Black Claw - 4 bosses leading up to the final boss.
Ragyou = Sister Jill - the imposing female Big Bad.
The last scene of the beginning credits features a gloved hand evidently grasping air, with details that suggest it may be a shoutout to Asuka's famous "I'll kill you" scene. Which, given the staff and the context of the story, might not be too far off.
The first ending is almost scene-to-scene identical to the ending of the 1985 live action version of the manga Sukeban Deka, as seen here◊.
The ending credits list Guts, the Mankanshokus' dog, as voiced by "?" - Gainax already did this in FLCL where Miyu Miyu, Naota's cat, was credited as voiced by "?" (eventually revealed as Hideaki Anno).
The decision to translate Shitennō as "Elite Four" is likely a reference to Pokémon. They even challenge Ryuko to a Boss Rush in episode 8.
Honnoji Academy has a tall tower overlooking the school grounds similar to Ohtori Academy.
Honnoji City has a spiral highway going around it, Mako has a spiral watch, guess what other anime made by the creators also used spirals?
Each one of the Elite Four's Goku Uniforms has a Shout Out to the most well known works the staff of Studio Trigger produced.
Blade Regalia: FLCL - The giant robot/desperado/hand with a weapon on each finger.
Senketsu, on the other hand, bears an uncanny resemblance to Mazinger Z◊.
The X symbol on the soldier's "uniforms" of Nudist Beach is identical to the X symbol used by the X-Men. Particularly the ones from the the X-Men cartoon from the 90's. Though here the X represents their hatred of clothing; Their flag is a red X over a pair of underwear. Whereas in X-Men it was a symbol for Charles Xavier.
Episode 1: "If Only I Had Thorns Like a Thistle..."
The episode's title is taken from Miyako Chaki's "Azami no gotoku toge areba" (YouTube).
Satsuki's first lines (see Double Speak above) are taken almost verbatim from 1984.
Satsuki refers to the other students as pigs in human clothing, perhaps a reference to a certain novel that also deals with themes of totalitarianism and inequality.
Ryuuko's first scene in episode 1 where walks across a bridge into town, get harassed by neighborhood gangs, beats them up thereby earning respect is straight out of Ashita no Joe.
Ryuko carrying her Scissor Blade in a guitar case and her search for revenge for the death of a loved one is an apparent shout-out to Robert Rodriguez's Desperado.
The scene where Ryuko lands onto the pile of cloths at the secret basement of her house bleeding, and then awakening Senketsu from below in search of the blood's owner, is practically identical to how Teppei metX in Masami Kurumada's Bt X.
Mako uses the Kinnikuman Kinniku Buster on Mataro.
Mako and Ryuko getting crucified (or pinned/hung) upside down is similar to how Mayumi Takahasi gets tied up in Kekko Kamen.
The Akio◊ Car makes an appearance. Not only is the car nearly identical, but the route they take is nearly identical to the one Akio drove around when making his speeches.
Gamagoori's driving in episode 8 may be a Shout Out to the Panty & Stocking with Garterbelt episode "Death Race 2010", where the car ghost wiped out the Daten City police cars by spinning. How the Daten Police tried to subjugate the ghost by ramming into it is also replicated.
Episode 9: "A Once in a Lifetime Chance"
The episode's title is taken from Hideki Saijo's "Chance wa ichido" (YouTube).
The city where REVOCS HQ is situated has the company logo, a blood red logo with the name of the company in capitalized letters, on the facade of every tower, like NERV's leaf was on all of Tokyo-3's buildings.
Then the camera shows the "cone-shaped" base of REVOCS building at an angle that make it looks like a pyramid, reminiscent of NERV's HQ pyramid.
Ragyo's speech mentions mankind's original sin and the Fruit of Knowledge, two themes often presents in Gendo's dialogs.
Ragyo's personnal office is basically a circular version of Gendo's famous office, with the complete lack of furniture except a lone desk, strange marking on the ground and ceiling and windows circling the entire office providing the only source of light.
REVOCS itself, a sinister multinational god-building think tank answerable to apparently no one, is actually a mere front for COVERS...an even more sinister multinational god-building think tank answerable to apparently no one, exactly like NERV was a front for SEELE.
Mako's brother and dad running in circles until they turn into butter is a reference to Little Black Sambo.
Nui's ability to create and operate human-like puppets with strings of Life Fiber reminds of Leonof the Puppetmaster from Trigun, who similarly created extremely lifelike puppets and moved them with strings.
Episode 14: "Ride Like the Wind"
The episode's title comes from Takao Hirata & Cellsters' "Isoge Kaze no you ni" (YouTube).
The big tusked turtle guardian brings to mind a certain other guardian turtle.
A villainous force invades Osaka militarily. The citizens of Osaka harness their community power and keep the bad guys at the gate. That is one of the battles in Burst Angel.
Inumuta appeared as a very Star Wars-like blue hologram.
Did Mako channel Kenshiro to catch all that money being shot at her?
Episode 15: "Don't Stop Me Now"
The episode's title comes from Linda Yamamoto's "Dō ni mo Tomaranai" (YouTube).
This may not be a fully intentional one and more of a coincidence, but Satsuki's escape and fighting COVERS with her feet brings to mind the naked Raiden gameplay segment of Metal Gear Solid 2: Sons of Liberty.
The scene where Gamagoori jumps from a helicopter and lands in front of Satsuki is based on a scene from FLCL where Naota and Lord Canti jump down and land in front of Mamimi.
Episode 21: "Incomplete"
The episode's title comes from Hiromi Gou's "Mikansei" (YouTube).
At the end, when Ryuko rips her way out of Junketsu, after a brief trip inside her mind, we are treated to some shots that look suspiciously similar to Episode 16 of Neon Genesis Evangelion, after Unit 01 bursts out of Leliel and stands soaked in a rain of blood.
Episode 22: "Tell Me How You Feel"
The episode's title comes from Machiko Watanabe's "Kuchibiru yo, atsuku kimi wo katare" (YouTube)