Defictionalization: Long before its official release in the card game, there was another version of the Seal of Oricalchos but there were only 15 in the entire world, used in a single special tournament by Upper Deck employees where players could duel them. And yes, their version was just as overpowered as it was in the show, which is why the legal version got nerfed.
Truth in Television: Remember Pegasus, the guy who had those overpowered Toon cards that were never released into circulation due to being too strong?
Fountain of Expies: The particular style of outfit Dark Magician wears has inspired an entire archtype of Magician cards, and of course he has many evolved forms.
In a roundabout way, it's now tradition for the protagonist's key monster to have 2500 Attack, while to parallel the Blue-Eyes, their rival's key monster has 3000 Attack.
Dark Magician Girl. Let's see: Magician's Valkyria, Gagaga Girl, Magi Magi Magician Gal, and Card Ejector.
The mighty Blue Eyes White Dragon: Cyber Dragon, White Night Dragon, Red Dragon Archfiend, and especially Galaxy Eyes Photon Dragon, most of which are played by major rivals and have equivalent attack and/or triple-fusion or Xyz variants. See below.
And for Blue-Eyes Ultimate Dragon, we have Cyber End Dragon, and Neo Galaxy Eyes Photon Dragon. (Though the latter differs in that it is a triple level 8 material Xyz monster.)
One can think of Red Nova Dragon as a Expy to BEUD as well considering that just to summon red nova takes 2 tuners, meaning he usually has 4500 or more attack.
Homage / Shout-Out - The game started off as a homage to Magic: the Gathering for the Yu-Gi-Oh! manga. On top of that, several of the cards also reference various of Konami's video game franchises, most notably the Gradius video game series (not to mention a very special appearance from Metal Gear Solid).
Apparently, Hideo Kojima, creator of the Metal Gear Solid series, has expressed interest in the game, and as such is called "Hideojama" in reference to the "Ojamas". The Metal Gear reference is probably a shout back at this.
To stop beating around the bush, Tactical Espionage Expert is a near physical double of either Solid Snake or Raiden, and his name comes from the series's subtitle: "Tactical Espionage Action".
Also, in the set of cards based on Tarot Greater Arcana, the card representing The World has the power to, effectively, stop time by giving you potentially unlimited turns — a shout out to Dio Brando's famous stand of the same name from JoJo's Bizarre Adventure.
The ability of Gladiator Beast monster to switch places with another Gladiator Beast from the deck after battling has been unanimously dubbed "Tag Out" by the playerdom.
The Elemental Heroes, or at least the earlier non-Fusion ones, are based on various American superheroes (Avian / Hawkman, Bladedge / Iron Man, Necroshade / Spawn).
The Elementals weren't the only ones: Destiny Heroes, two in particular, were based on two chracters in classic Novels (Double Dude/ Dr. Jekyll and Mr. Hyde; Dreadmaster/ The Man in the Iron Mask) and one Evil Hero is based on one of the X-Men (Malicious Edge/Wolverine).
And the Masked Heroes as a whole are nods to the Kamen Rider franchise.
More specifically, the Inzektor monsters design, and their overall effect of a stronger armoured Inzektor over a lighter faster Inzektor is a shout out to Kamen Rider Kabuto.
Several cards use characters from other Shonen Jump series.
While the Yu-Gi-Oh! TCG is itself based off Magic: The Gathering, very few cards from the former actually reference the latter... except for the Prophecy archetype. The Prophecy Destroyer's art style is very Magic-esque, while Wheel of Prophecy could be an Expy or Captain Ersatz of Ajani Goldmane, a Planeswalker from the Magic universe. Temperance of Prophecy can also be said to resemble Jace Beleren.
And the other way around works, too. Check out the Silent Swordsman and Silent Magician. Now look at Kargan Dragonlord and Guul Draz Assassin... and Chandra Nalaar's Japanese Duel Deck art.
"Galaxy-Eyes" monsters - Photon Dragon, Tachyon Dragon, Neo Photon, Neo Tachyon and Prime Photon...
Gandora the Dragon of Destruction
Garlandolf, King of Destruction
Hamon, Lord of Striking Thunder
Infernity Doom Dragon
Legendary Six Samurai Shi En
Metaion, the Time Lord
"Monarch" (Specifically, any card that ends in Monarch - Mobius, Thestalos, Granmarg, Zaborg, Kuraz, Caius, Delg, and RAIZA.)
Obelisk the Tormentor
Ocean Dragon Lord - Neo Daedalus
Possessed Dark Soul
Raviel, Lord of Phantams
Red Eyes Darkness Metal Dragon
Red Nova Dragon
Reshef, the Dark Being
Ruin, Queen of Oblivion
Sephylon, the Ultimate Time Lord
Superancient Deepsea King Coelacanth
Shinato, King of a Higher Plane
Shooting Quasar Dragon
Slifer the Sky Dragon
Sophia, the Creator
"The Beginning of The End" spell card
The Tyrant Neptune
The Wicked Avatar/Dreadroot/Eraser
The Winged Dragon of Ra
Thousand Eyes Restrict
Trishula Dragon of Ice Barrier
Uria, Lord of Searing Flames
Venominaga the Deity of Poisonous Snakes
Yubel - Terror Incarnate
Yubel - The Ultimate Nightmare
Urban Legend of Zelda: 2ch users created a hoax so convincing, it tricked Japanese Yu-Gi-Oh! fan sites. The hoax basically stated that Lightsworn were dolls who were slaves of an evil force.
Viewer Gender Confusion: Red ponytail, feminine face, slim physique, it's very inconclusive, especially as some cards draw him as a more typical "Buff" warrior, while others draw him like a Bishounen, Common consensus is that there's multiple Black Luster Soldiers.