By the way, here's the updated version of the Wikipedia article:
The XIII Order is a group of thirteen Non-Existent Ones featured in the PlayStation 2 role-playing game Kingdom Hearts II. They were originally introduced as The Organization in the game Kingdom Hearts: Chain of Memories. They seek to discover the mysteries that lie within the Heart and use the power of Kingdom Hearts to become human once more. Each Order member controls their own element and their own breed of Nobodies. Judging by evidence presented in the game Chain of Memories, the members are numbered by the order in which they joined the group.
Known Members and Their Rankings
1. Enigmatic Man - A mysterious Unknown whom Sora fights in the Final Mix version of the original Kingdom Hearts at Hollow Bastion. According to Nomura, he is the man standing in the center of a group of five members of the Order in a scene from a trailer released back in 2003, meaning he is probably very high ranked. Other than this, the only thing known about him is that he can manifest some sort of energy as a weapon (One of the ways he uses it is by making red "swords" with it, which some fans half-mockingly referred to it as lightsabers.) and move through solid objects such as humans. It is likely that he will be one of the main villains of Kingdom Hearts II.
2. Unknown
3. Xaldin (English spelling unconfirmed) -- Xaldin confronts Sora in Beast's Castle when he threatens to destroy Beast's mystical rose and forces Beast to fight for him. A master of wind magic, he wields six lances, naginatas, and he sports long black hair and long sideburns. There is a screenshot of him saying, roughly translated, "Once we obtain Kingdom Hearts we will become complete beings!"
4. Vexen -- One of the older members of the Organization, Vexen is a scientist and, using data he collects, creates a replica of Riku. While he agrees to Marluxia's demands, in truth, Vexen intends to betray him. He wields a shield and controls the element of ice.
5. Lexaeus -- Along with Vexen and Zexion, Lexaeus conspires against Marluxia. He intends to use Riku as Marluxia had intended to use Sora. Lexaeus wields a tomahawk and controls the element of earth.
6. Zexion -- Zexion is almost as skilled a manipulator as Axel, though as we discover, not enough. He is content to watch Lexaeus and Vexen do all the work, but finds he must come from the shadows when his allies fail. He is the only member of the Organization observed thus far with the ability to detect the presense, absence, or death of individuals by their scent. His element is unknown but may be illusion or of a psychic power.
7. Unknown
8. Axel -- Axel is a manipulator, new to the Organization. He worked for Marluxia in Kingdom Hearts: chain of Memories, yet only seeked to benefit himself and his amibgious plan. He wields Fire Chakrams and controls the element of fire. He mentions he has some connection to Sora. Of the Organization members seen in Kingdom Hearts: Chain of Memories, Axel is the only one to survive. He killed Vexen personally and ordered the Riku Replica to destroy Zexion.
9. Demyx -- He appears as a young man with brown hair who appears in the Underworld. His weapon resembles a samisen. He controls the element of water.
10. Luxord (English spelling unconfirmed) -- A man first seen at Port Royal. He has white hair, a mustache, several earrings, and uses a deck of 52 playing cards as his weapon. It is rumored that he controls the element of time.
11. Marluxia -- The lord of Castle Oblivion and a relative newcomer to the Organization. He intends to usurp the order by capturing and manipulating Sora, using Naminé to do so. He wields a pink scythe and controls the element of nature.
12. Larxene -- Also a newcomer to the Organization, Larxene conspires with Marluxia to capture and manipulate Sora for their own purposes. She has an abrasive personality and caustic tongue, but is on best terms with Axel. She wields several small kunai and controls the element of lightning.
13. Unknown
Members with Unknown Ranks
?????: A man with long blue hair summoning his Nobodies at Hollow Bastion.
?????: A man with spikey silver hair in the area of the War Sequence. His voice is very similar to the Enigmatic Man's.
Xigbal (English spelling unconfirmed): A recent magazine scan has discovered another member of Organization, he wears a black eye patch similar to a pirate, a scar on the left side of his face, and holds two fan blades. It is rumored that he controls the element of gravity. The scan shows what looks to be him in the Land of Dragons.
Possible Members
BHK - He was seen wearing the order's robe in Another Side, Another Story and Deep Dive with his keyblades, Oathkeeper and Oblivion.
Mickey Mouse - King Mickey was seen with Riku wearing robes almost similar to the XIII Order's at the end of Kingdom Hearts: Reverse/Rebirth as well. According to DiZ, he and the King have met before. Therefore, due Mickey's confusing role in Kingdom Hearts and Kingdom Hearts: Chain of Memories, it cannot be ruled out that he was an earlier member. In the most recent trailer he is seen taking off his cloak, meaning that probably he is not a member of the Order after all, although the evidence to this is debatable.
Riku - At the end of "Kingdom Hearts: Chain of Memories'" Reverse/Rebirth storyline, Riku began to walk the "road to dawn", using both Light and Darkness and is wearing the XIII Order's uniform, but it is unknown if he joined the XIII Order itself. Also, during the "Another Side, Another Story" teaser trailer, two people wearing Order coats are seen fighting Heartless. One of them has long, silver hair and a blindfold, and has been confirmed to be Riku.
DiZ - An enigma who, according to sources who viewed the 8 minute 30 second trailer at the July 30-31st Square Enix Party 2005, seeks out BHK as a means to eliminate the XIII Order. He has been shown in conversation with the Enigmatic Man as well.