Black coat

The black coat (黒いコート), also called the black cloak, is a magical form of clothing that allows the person that wears it to safely pass through the Corridors of Darkness; appearance-wise, it is simply a black long-sleeved, double-breasted, twin-tailed trenchcoat with a hood. It has a large silver zipper that fastens at the top and zips down to seal the coat. It has silver drawstrings for the hood decorated with a large silver bead hanging from the end and a silver chain ornament adorned with four large cylindrical silver beads that fastens to a loop on either side of the collarbone region.

It is most noticeable as the uniform for Organization XIII, but it is first used by Master Xehanort in Kingdom Hearts Birth by Sleep as an alternative to the Keyblade wielders' traditional armor. Several characters outside of the Organization wear this coat, including Riku, King Mickey, Ansem the Wise, Anti Black Coat, and a Moogle.

The Black Coat's main purpose is to resist the corruption inflicted upon one's heart when they pass through a Corridor of Darkness. It also seems to be able to change shape to fit its wearer, as seen when Xion shifts from her normal form to Sora's, and when Riku changes into his Ansem form.

Somehow, when Riku and King Mickey cast their coats off, the black gloves, pants, and boots worn under the coat disappear. Furthermore, any trace of the wearer's clothing under the coat disappears, such as Riku's collar, jeans, and sneakers in his second attire, or Mickey's trademark white gloves. All these hint that donning the coat transforms whatever clothing the coat's bearer is wearing under it into the black gloves, pants, and boots seen on all the coat's wearers. However, Roxas's sneakers are visible under his coat in several of his appearances.

Development
The black coats were originally designed for Roxas and Riku in the secret video Another side, Another story... simply as a way to disguise them while they were still being designed for Kingdom Hearts II. It was again used simply to hide Xemnas's face during his optional boss battle in Kingdom Hearts Final Mix and in Deep Dive, starting the trend of all Organization members wearing it. Nomura stated in an interview that his initial idea for "The Gathering" was to have Terra, Aqua and Ventus wear similar coats to the Organization XIII coats to hide their at-the-time undesigned faces, but felt that he could not use black coats once again, and so chose armor instead.

Kingdom Hearts Birth by Sleep
Master Xehanort is seen wearing a black coat as he leaves Ventus, wrapped in white cloth, on Destiny Islands.

Young Xehanort, also wearing a black coat, later appears at the Land of Departure and battles Terra, Ventus, and Aqua, only to lose and depart.

Kingdom Hearts Final Mix
The Unknown is seen wearing the black coat when he fights Sora in Hollow Bastion.

Kingdom Hearts 358/2 Days
All of the Organization members, Roxas, Riku, Xion, and Mickey wear the coat. The Moogle who becomes available to purchase items, also wears the black coat, as a sign of it servicing Organization XIII.

Kingdom Hearts: Chain of Memories
Riku and King Mickey are given Black Coats by DiZ, who obtained them through unknown means, so that they would not be tracked down by Organization XIII. Riku continues to wear the coat until the explosion of the Kingdom Hearts Encoder at The World That Never Was.

Kingdom Hearts II
All the members of Organization XIII wear the black coat. King Mickey also dons the black coat until taking it off later in the game, and Riku is seen wearing it while taking the appearance of Ansem, Seeker of Darkness. He takes it off after reverting back to his original form. The Mushroom XIII are also seen wearing the coat.

Kingdom Hearts coded
Jiminy's Journal takes on the form of Riku when the latter was wearing an Organization XIII coat.

Blank Points
When Aqua comes across Ansem the Wise at the Dark Margin in the Realm of Darkness, he is wearing a black coat.

Kingdom Hearts 3D: Dream Drop Distance
Following his restoration after Axel's death, Lea sports the Black Coat his Nobody once wore. Young Xehanort continues to wear the Black Coat, though this time with the hood down. The Anti Black Coat wears the coat, though with magenta colorations on the neck and sleeves. A Riku that appears inside Monstro also wears the coat.

Organization XIII
Among the most notable characters that sport the black coat are the members of Organization XIII. The Organization's coats are not uniform in appearance. For instance, Axel's coat has tight sleeves, while Xigbar and Demyx both wear coats with pointed shoulders. Additionally, Vexen's coat is longer than most other members, to the point that it covers his feet and its sleeves partially cover his hands. Roxas and Xion in Sora's form wear what appear to be black sneakers, while Larxene and Xion in her normal form wear heeled boots.