The entire game is crammed with them, to the point that it's easier to list which parts of the game aren'tShout Outs. Also, we have nowhere near all of the shout outs, so this page will take a very long time to be finished. A bunch of examples, sorted by reference subject:
Anime and Manga
If a player gets more than 9000 kills online, his profile will read "Kills Over 9000".
One of the challenges for inflicting damage is "Human Tsunami". In the series, the main character is believed to be so destructive, he's classified as "The Humanoid Typhoon", making him the first human being to be registered as a natural disaster.
The black Runner color-scheme names it "Vehicle X". The black Racer is the X-Racer.
Interplanetary Ninja Assassin Claptrap's habit of calling humans "Fleshbags" may be a reference to Lexx, in which the cannibalistic Giggerota refers to other humans as such. Alternatively, it may be a reference to something else entirely (see the Video Games entry below).
During the quest he appears in, the Player Character has to collect poisoned cigars because "some kid could find them".
The game even has pure visual shoutouts — the Crimson Lance comes with posters that reference District 9. Considering D9 came out only a few months before the game did, Gearbox was essentially adding in new art assets and shoutouts right up to the last possible moment.
The Chiquito Amigo's 'Say "Hello"' caption seems innocuous enough, until you take into accound that Chiquito Amigo translates as 'Little Friend' to which you realise its a subtle reference to Tony Montana's infamous line "Say Hello To My Little Friend!"
The quote for the Hyperion Invader "BAM BAM BAM BAM BAM!" resembles a scene in the movie Reservoir Dogs where hired gun Mr. White, furious at Mr. Blonde's earlier shooting of several hostages, re-enacts the scenario by using his hand as a gun and shouting "BAM! BAM! BAM! BAM!"
"I have you in my eye, Sir" for the Atlas Cyclops sniper rifle is from a line by Dr. Willis warning George III to do as he's told in the the 1994 film The Madness Of King George.
You also fight a unique Spiderant boss named "Helob".
In the Zombie Island of Dr. Ned DLC, one of the things Zombie TK can say about brains when you enter his house is "Boil 'em, mash 'em, stick 'em in a stew."
The Secret Army of General Knoxx DLC takes you to the Pipp Inn.
There are a large amount of Shoutout to The Hitchhiker's Guide to the Galaxy. One of the Claptraps you can rescue repeats nearly word-for-word Marvin's speech when he first meets Arthur Dent. And I've seen a couple of signs that say "Don't Panic", in large friendly letters to boot.
Tannis needs you to get parts for her Infinite Improbability Drive in Claptrap's New Robot Revolution.
Written on the walls of some of the early houses are the words "turtles all the way down".
Whitting's Elephant Gun could be based on Ernest Hemingway's "Hills like White Elephants". Evidence of this includes: 1. The gun's name is "Whitting's Elephant Gun", which could reference "Hills like White Elephants" 2. Ernest Hemingway was a noted "Big Game Hunter", which is also the title of the mission where you have to kill Skagzilla, which leads to you acquiring the gun as a reward and 3. The mission is given by a man named Ernest Whitting.
In the second game, Axton has an ability in his Gunpowder tree called Ranger. Its icon is two crossed rifles resembling the M16 with a star next to the top, left and right sides of the rifles. The Real Life U.S. Army Rangers do not have any sort of logo, but they get a similar one◊ within Call of Duty: Modern Warfare 2.
The Powered Armour suits used by the crimson lance in the latest DLC look an awful lot like Adeptus Astartes power armour, also the suits care called 'devastators' which happen to be names of the Adeptus space marines who carried the biggest guns.
Once the Crimson Lance start spawning in the Salt Flats, they are surrounded by what look like very thinly disguised Space Marine drop pods.
Memes / Internet Culture
The Final Boss of the Robo Revolution DLC may sometimes say "Looks like you're writing a suicide note. Would you like some help?" as a shout out to the infamous Microsoft Word mascot helper, Clippy.
A potential self-referential Shout-Out: During Mad Moxxi's Underdome Riot, if you kill a Bandit with a headshot using Revolvers, the crowd will cheer "Heyooo!" in response.
Mad Moxxi's first husband is described as a cheat. In the cutscene, he is killed with the Konami Code.
Tarot cards get a shout out when you find T.K. Baha's body in a position almost exactly like The Hanging Man.
The Atlas Patton. ("May God have mercy on my enemies, because I won't" was supposedly said once by General George S. Patton, hence the name. The Other Wiki claims it was also once uttered by Queen Elizabeth the First.)
Double reference in that the Patton always spawns as a revolver with a nickel-plated body and an ivory grip, referencing the two revolvers (in the same style) which Patton himself owned.
Roland and Axton have an ability called Metal Storm, which is also the name shared by a weapons company.
Whitting's Elephant Gun: an Elephant Gun is actually a real life type of rifle for hunting big game (e.g. elephants), Skagzilla could easily be classified as such.
The green Runner palette, "Mean Green", has a strong resemblance to a P40 Warhawk◊.
In DLC 3, at "Road's End", the player will spot a highway sign reading "Fort Knoxx - 20km". Fort Knox is an actual United States Military post, known for its proximity to the United States Bullion Depository. General Knoxx's unique, highly-valuable pistol ("Knoxx's Gold") is a further reference to this location.
There is a location on Pandora known as "Treacher's Landing", which is a possible reference to Arthur Treacher's chain of seafood restaurants.
One of the challenges for scoring kills is titled "Your Kung-Fu is Best". This is a reference to Kevin Mitnick, a computer security consultant and author. He was previously a well-known computer hacker and 'phreaker', and prior to his arrest, he left a message on the investigating detective's answering machine, stating "My kung-fu is best!"
Another challenge (this one for dealing Shock damage) is titled "Nikola Tesla is a friend of mine."
Yet another (for sheer number of enemies killed) is titled "Now I am become Death...", a phrase uttered by J. Robert Oppenheimer.
Additionally, Sander's Gorge is a prominent location in the Robot Revolution DLC, and even contains Cluck-Trap — a Claptrap that looks like a chicken. Also, upon entering the gorge for the first time, Interplanetary Ninja Assassin Claptrap has this to say:
More than a few brave men have turned chicken at Sanders Gorge... and even more have made that truly awful joke.