"Screw the rules, I have money!" came from this fan series.
Yugioh Abridged
The fifth series in the anime.
Arc-V
The owner of this deck archetype
Tristan Taylor
This deck type was used by famous American duelist Bandit Keith, but had to be censored heavily due to the fact it contained too many guns, and included Keith himself pointing a gun at Pegasus' head.
Machines
Pot of Greed allows you to draw this many cards.
The meme "card games on motorcycles" was made canon by this character in the movie Bonds Beyond Time
Yusei
This Nazca line discovery was predicted by the 5ds anime
a snake
Named after a capacity of data, this is the main character of the Gigo deck archetype storyline.
Gigobyte
The signature card of this deck was created by launching a time capsule into space, with a child's drawing inside, that passed into another dimension near Jupiter.
Neo-Space Aqua Dolphin
Who owned the 4th and final copy of Blue-Eyes White Dragon?
Yugi's Grandpa.
This card forces your opponent to accept an IRL handshake or lose the duel.
Yu-Jo friendship
5-headed dragon is the final boss in this arc of the original series.
Virtual World Arc

Gogiga Gagagio
The monsters featured in this deck type were responsible for giving their owner an addiction to electroshock pain, and eventually resulted in him dying from heart failure.
Cyberdarks
4Kids censored this many deaths across all seven anime series. (Bonus points if you can name how many were in the first series)
57 (24)
This military prison was destroyed by Seto Kaiba to build the Duel Tower
Alcatraz
Gansley, Crump, Johnson, Nezbitt and Leichter.
The Big 5.
Pronounce this: Xyz
"Ik-seez" (sounds like exceeds)
This overarching type featured dragons bounded to people called 'Signers' who helped seal a tremendous evil capitalist inside the Nazca Lines via playing Duel Monsters on Duel Runners.
Legend of the Crimson Dragon
The number of cards that have flavor-text only errata.
3
The original purpose of the Duel Monsters Hologram technology pioneered by KaibaCorp and later Pegasus.
War simulation and combat training.
This card requires 5 human sacrifices to harness the 5 specific emotions of Anger, Hatred, Anguish, Sadness & Doubt
Super Polymerization
Abbreviated on most card prints as D/D/D/D, this deck archetype was original introduced by Numbers holder Nelson Andrews, and makes up a large majority of the longest card names in the TCG.
Different Dimension Demon Deity
This deck was used to steal souls in Penalty Game duels which would feed the primordial serpent and raise Atlantis from the bottom of the sea.
Orichalcos
The number of times the card game has been referred to as Yu-gi-oh! in the anime series.
1