The Parasite Cage Heartless in the first game bears many similarities to an early boss in Final Fantasy IX, Prison Cage. In both games, a character (Pinocchio in Kingdom Hearts and Garnet, then Vivi, in Final Fantasy IX) gets trapped inside the creature, and the main character (Sora/Zidane) must work together with his at-the-time enemy (Riku/Steiner) to free them. Both enemies are fought twice in total. Vivi and Pinocchio also share some similarities, as Pinocchio is a puppet who possesses a heart and a conscience, and Vivi is an artificial lifeform who also possesses a conscience and "heart".
In Kingdom Hearts II, after Tron puts in the password for the DTD, the MCP attacks the party with a bolt in a matter similar to the lightning bolts of Final Fantasy X. The reactions of everyone is also similar to that game, where Tron manages to dodge by jumping back, but Sora, Donald, and Goofy are struck, with the latter two flipping from the recoil.
The first Formchange for the Wheel of Fate Keyblade in III is called "High Wind" and is a spear, referencing the famous Dragoon class and its Theme Naming from the Final Fantasy series. The weapon's combo finisher is also heavily inspired by the Dragoon's Jump ability.
To other franchises:
The Darkside Heartless is named after Tales from the Darkside, an anthology horror TV series. The Twilight Thorn is called Twilight Zone in Japanese, referencing another famous horror TV series.
Part of End of the World from the first game seems to have been inspired by Nowhere.
Xigbar's title, "Freeshooter", is taken from the title of the German opera Der Freischütz. The eponymous marksman makes a Deal with the Devil in exchange for seven magical bullets; the first six are controlled by the marksman while the seventh is controlled by the Devil.
In Kingdom Hearts: 358/2 Days, there's a set of weapons called Casual Gear. When this is equipped, Demyx's sitar turns into a tennis racket. Its name? Prince ofAwesome. Another of Demyx's weapons in Days is called "Up To Eleven".
The last Gummi route in II, Assault of the Dreadnought, is a direct homage to Star Wars, particularly the Death Star battles in A New Hope and Return of the Jedi. Likewise, as a continuous homage to the theme naming from the Final Fantasy series, two shopkeepers (one in Twilight Town, the other in Hollow Bastion/Radiant Garden) are named after Biggs Darklighter and Wedge Antilles, though the presence of Jessie confirms they are based on the Biggs and Wedge of Final Fantasy VII, instead.
Terra's story in Birth by Sleep is a homage to Revenge of the Sith, right down to him succumbing to the dark side like Anakin Skywalker. Riku can even be seen as a parallel to Luke Skywalker, and Sora with Han Solo. Both Luke and Riku were tempted with the dark side, and succeed with what their father/predecessor failed: becoming a Jedi/Keyblade Master. Meanwhile, both Han and Sora take on Non Human Sidekicks with a Cool Ship, and spend a year frozen in carbonite or sleeping in a pod.
When crushed by the painting of Ansem (really Terra-Xehanort) in the manga adaptation, Sora mutters "Ansem strikes back".
The trophy for completing all the Gummi Ship courses in KH1:FM or getting an S-rank on all EX Gummi Ship missions in KH2:FM is called " Top Gun "
The trophy for winning 100 duels in Re:CoM is called " Duel Master "
Young Xehanort belts out a "TOKI YO TOMARE!" in the Japanese version of KH3D when he momentarily stops time to rewind to the start of the boss battle. He also has an attack where he generates icicles that after a brief flash of light, are inexplicably going to converge on Riku.
Also considering this point it's very possible that Ansem's Guardian Heartless is also a shout-out to stands.
In the manga adaptation for Kingdom Hearts: Chain of Memories, Doraemon and the Anywhere Door is mentioned when Sora and his friends enter the memory-based version of Traverse Town.
Look at the cover of Kingdom Hearts 1.5 and notice the throne Sora is sitting on. Not that different from another throne also made out of swords, right?
Tinker Bell is a fairy that can heal Sora, as well as be used as an extra life. Think she moved to Neverland from a certain other land? Especially noteworthy is the fact that a certain blue fairy companion of Link's has been noted to be a parallel of Tink's, since both are fairies who have feelings for their partners (Link for Navi, and Peter Pan for Tink), and are jealous of another girl close to them (Princess Zelda and Wendy Darling, respectively).
The keychain that Sora obtains in Halloween Town in the first game (and later as an Attack Card in CoM) is named " Pumpkinhead "
In Kingdom Hearts II, the only way to get to Yen Sid's Tower is by a mysterious train in Twilight Town, much like the Wizard's special subway train in Shazam!. Becomes Hilarious in Hindsight in 2019, when Zachary Levi (Flynn Rider) is cast as adult Billy Batson in the DC Extended Universe film.
Yen Sid's name is an homage to Walt Disney, and not in the way it originally seems; while "Yen Sid" is indeed "Disney" spelled backwards, Walt Disney himself would use the Sdrawkcab Alias "Retlaw Yensid" when involving himself in projects and media that he did not want the public to know about.note For example, he called himself by this alias while scouting Florida for the property that would eventually become Walt Disney World, due to knowing that if the real estate owners knew just who was looking for land, they might try to up-sell him unsuitable property for the theme park.
The Trophy/Achievement earned from defeating Schwarzgeist in III is named after its theme from its origin game.
In Monstropolis, Sora's fur color will become yellow with orange stripes if he Formchanges into Guardian Form, making him resemble a lombax. For bonus points, one of the Guardian Form Keyblades, Hunny Spout, transforms into guns.
. The eponymous marksman makes a Deal with the Devil in exchange for seven magical bullets; the first six are controlled by the marksman while the seventh is controlled by the Devil.