I. Xemnas - Defeated by Sora and Riku at the end of Kingdom Hearts II. He was trying to dispose of the only threat standing between him and Kingdom Hearts. Disappeared in Darkness in what appears to be a black variation of the white Nobody thorns. He was the thirteenth and final member to fall, but since both his Heartless and Nobody have been slain, Master Xehanort is now able to return from the darkness.
II. Xigbar - Defeated by Sora, Donald, and Goofy in the Hall of Empty Melodies in The World That Never Was. He started the fight to try to prevent Sora and company from ascending any farther up the castle but disappeared into Darkness. He was the ninth member to disappear.
III. Xaldin - Defeated by Sora, Donald, Goofy, and Beast at Beast's Castle. He was on a mission to turn the Beast into a Heartless and Nobody. Disappeared into Darkness and wind. Xaldin was the seventh member subject to elimination.
IV. Vexen - Defeated by Axel as a way to gain Marluxia's trust. Vexen opposed Marluxia's plot and Marluxia wanted him eliminated. Disappeared by incineration into Darkness. He was the first member to fall.
V. Lexaeus - Defeated by Riku while possessed by Ansem, Seeker of Darkness. He was trying to make Riku use the Darkness inside him. From what is shown in the cutscene of his elimination, he was helpless against Ansem, Seeker of Darkness due to his weakened condition after his brutal fight with Riku. He disappeared into Darkness, and was the third member eliminated.
VI. Zexion - Defeated by Riku Replica and Axel. Axel wanted no evidence of his actions in Castle Oblivion, so when Zexion was extremely weary from his battle with the real Riku, Axel had the Riku Replica absorb Zexion. He disappeared into gaseous Darkness while engulfed in the Replica's energy. Zexion was the fifth member to fall.
IX. Demyx - Defeated, by Sora, Donald, and Goofy. He was one of the few mentionable people destroyed in the Battle of the 1000 Heartless. He confronted Sora and company just for the sake of battling in the war. He disappeared into Darkness and appeared to have boiled up and evaporated. He was the sixth member to disappear.
X. Luxord - Defeated by Sora. He captured Donald, Goofy, Riku, and Kairi, forcing Sora into one of Luxord's "games." Sora was able to beat him by "winning the game" and slashing through his shield of cards. He disappeared into gaseous Darkness. Luxord was the tenth member to be eliminated.
XI. Marluxia - Defeated by Sora. He was trying to destroy Sora since he couldn't control him. Marluxia himself is never actually fought, but after Sora destroys a clone, a machine-like Nobody and an angel-like, feminine reaper, all Marluxia's energy is gone and he is beaten. He disappeared attempting to grab Sora in gaseous Darkness in a flurry of flower petals. Marluxia was the fourth member to disappear.
XII. Larxene - Defeated by Sora, Donald, and Goofy. She was on a mission to kill Sora after her plan fell apart. She would have succeeded, but an attempt to save Sora by Naminé, Donald, and Goofy gave him the strength to fight back, and Larxene eventually met her end. She disappeared into Darkness. Larxene was the second member to fall.
XIII. Roxas - Arguably the only surviving member. Roxas permanently sealed himself within Sora just before the final battle with Xemnas, willingly giving up his physical existence. Although he is not gone, he was the twelfth member to "fall".
XIV. Xion used the attribute of Light and the Kingdom Key Keyblade. Although she is referred to as the fourteenth member, she is not actually considered to be part of the Organization, and she is not a Nobody. She is an imperfect replica of Roxas created from Sora's leaked memories.
Although the Organization XIII are enemies to Maleficent, Padro Lodo forced her to revive them with heart shards because of their potentially devastating powers. The evil faerie agreed, and the Org XIII, well the really evil members, returned to battle Nick and Sora. After the two heroes defeated Xemnas, the XIII's essence somehow was released and intentionally revived by the Organization of Chaos to do their bidding, but later on, they were defeated again in the Chaos Emerald Arc. it's unknown yet when they will appear again since their essence has been collected and waited to be revived somehow by Hades or Sartana.
But this turns out to be a lot of bulk when it turns out that Lea, Even, Aeleus, Dilan, and Ienzo have already been revived as full humans and are now back on the side of light. Braig and Isa are also back as full humans, but they remain as villains because they are actually turning into clones of Master Xehanort due to him having gained the ability to shatter his heart at will and remove fragments of it into other peoples' hearts to overpower their own heart and grow a full heart of Xehanort. Xemnas, as it turns out, was actually working for Master Xehanort the whole time and had actually created the Organization XIII just to gather potential vessels for Xehanort's heart. He's currently resurrected by Master X to serve as a member of the 13 Hearts of Darkness, which are in cahoots with the Organization of Chaos. Of course, this still doesn't explain why Org XIII appeared before as Nobodies when they had all been destroyed and turned back into somebodies. The reason why they appeared before was because Immortus had used his time powers to briefly revive them from before their demise and reformation, allowing Maleficent to take control over them for their duration of their return to life. But now that Master Xehanort has unvieled his True Organization XIII, the originals can simply go to a trash bin for all he cares.