Fallout
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The full make and model of the 10mm pistols in Fallout and Fallout 2 is "Colt 6520 10mm pistol".
Starting with Fallout 3 and moving forward into New Vegas, the 10mm pistol is referred to as the "N99 10mm pistol".

They both fulfill the role of being a relatively common pistol for the wasteland, with a simple, easy to produce and replicate design. This is however, effectively a retcon to prevent legal issues with Colt.
Contributed by Psychospacecow
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According to the Fallout Bible, there are two vaults numbered "68" and "69." In Vault 68, there were 999 females and one male, with the exact opposite in Vault 69. The Vault numbers themselves are a reference to the corresponding sex positions and filled with the appropriate genders to match them.
Contributed by ThisGuyInTheSuit
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The design for Vault Boy was inspired by Rich Uncle Pennybags from the board game Monopoly.
Contributed by Pogue-Mahone
The in-game pre-war company called "Chryslus Motors" is a reference to the real-world company Chrysler Motors. They produce two car models; The Corvega and Highwayman.
The Corvega brandname is a combination of two Chevrolet cars, the Corvair and the Vega.

The Highwayman is likely another nod to the post-apocalyptic Mad Max movies. The Chosen One from Fallout 2 can obtain a drivable Highwayman, with a blower sticking out of the car's hood, and was originally going to have two-fuel tanks in the trunk, much like Mad Max's V8 Interceptor from Mad Max 2: The Road Warrior.
Contributed by G-Haven
The intro movie in the original Fallout is shown playing on a television with the label "Radiation King" during the game's opening. The name comes from the Simpsons episode "Grampa vs. Sexual Inadequacy", in which it shows a television with the same name that Homer Simpson watched from as a boy.

In Fallout 3, Radiation King becomes an established pre-war company, along with with an accessible store-building, that has televisions, radios and jukeboxes on display with the brand names on them.
Contributed by G-Haven
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Pinball machines found in Pilgrim's Landing from Fallout 3's "Point Lookout" DLC, as well as one in Jacobstown Lodge from Fallout: New Vegas, which has very worn out art/wording, have the word "White Star" written on them.

"White Star" is a reference to the White Star Board System, which is an arcade system board used for several pinball games designed by {(Sega)} Pinball and their successor, Stern Pinball, between 1995 and 2004.
Contributed by G-Haven
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The .223 Pistol in Fallout and Fallout 2 is modelled after Rick Deckard's handgun from the movie Blade Runner.

The gun appears again in New Vegas, named as "That Gun". According to Joshua Sawyer, the reason it was named that is because many players referred to it as "That Gun from Fallout and Fallout 2."
Contributed by G-Haven
The Deathclaw, an enemy present throughout the series, is a mutated Jackson's Chameleon (Trioceros Jacksonii) spliced with various other animal DNA. The mutation and splicing also eliminated their color-changing abilities.
Contributed by KidDivinegon
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Mentats, which temporarily increase a player's PE (Perception), IN (Intelligence) and CH (Charisma), are a direct reference to the novel series Dune, written by Frank Herbert.

In the novel, Mentats are super-intelligent human beings that undergo special training that gives them the cognitive and analytical abilities of electronic computers, replacing sentient machines altogether.
Contributed by G-Haven
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Grognak the Barbarian is an obvious reference to "The Savage Sword of Conan the Barbarian", and the cover of the in-game Grognak comic "In the Lair of the Virgin Eater" resembles the cover of the Conan comic named "Lair of the Ice Worm".

Also on the in-game comic cover, Grognak looks remarkably similar to the Barbarian class image from The Elder Scrolls IV: Oblivion. Notably the axe-heads, folds in the clothing, hand positions, and most of the body pose are almost exactly the same.
Contributed by G-Haven
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From the ideas carried over from Black Isle Studios' Van Buren to Fallout: New Vegas, there were two specific characters that made their way into New Vegas: Arcade Gannon and Joshua Graham. In Van Buren, both were recruitable companions for The Prisoner. Arcade has barely anything about him written, suggesting that he was written in only a short time before the project was cancelled, but Joshua Graham-- then called "The Hanged Man", was much more fleshed out. He was to be first encountered in Fort Abandon as a man completely wrapped in bandages and being hung by the neck from a pole, and was described as being one of the most evil characters in the game. With Graham's appearance in Honest Hearts, it seems that The Hanged Man's personality in Van Buren is what inspired Graham's particularly atrocious behavior as the Malpais Legate in his backstory.
Contributed by Sejii
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In both Fallout 1 and 2, if you were to enable "Large Icons" in Windows, the icons for Fallout and Fallout2 executables would turn in Tim Cain's head, who was one of the programmers and main designers for Fallout.
Contributed by G-Haven
In both Fallout 3 and Fallout: New Vegas, a weapon can be found called the Fat Man, a tactical nuke launcher. When you reload it, you hear a bell chime to indicate it has finished reloading. The sound heard is actually the Bethesda development team's lunch room bell.
Contributed by DidYouKnowGaming