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.