Axel

In Chain of Memories Axel seems to be involved in a plan with fellow members Marluxia and Larxene to take over Organization XIII. He killed Vexen on Marluxia's orders, right when Vexen was about to reveal to Sora an important secret regarding the Keyblade Master, which Axel and Marluxia could not allow. He remained a mysterious figure to Sora as he ventured through Castle Oblivion, only appearing as a cloaked figure when he first arrived to train him in the art of the strange cards they used there.  
 
Axel turned out to be a traitor to Marluxia and Larxene when he let Namine escape. He later confronts Marluxia, but does not defeat him. 
 
Axel appears again in Kingdom Hearts 2 after Roxas' fight with the Dusks. His plan was to knock Roxas unconscious so he could take the blonde back to Organization XIII. It is later revealed that he was Roxas' best friend and training buddy. Axel soon grew angered with Roxas for forgetting their friendship, and they engaged in a "heated" battle. Axel lost the fight, and made brief amends with Roxas before disappearing into the darkness. 
 
Number Eight does not appear again until late into the game, where he leaves the Organization behind in hopes of getting Roxas back. Axel's first step was kidnapping Kairi to use as bait for Sora, so that he could turn Sora into a heartless, thereby returning Roxas. However, Kairi proves to be more difficult to keep than he anticipated, and she soon escapes him (only to be caught by Saix). Axel appears in Hollow Bastion, and reveals information about Organization XIII to Sora, but before he could explain what happened to Kairi, Saix appears.   
 
Axel finally joins the "good" side and openly helps Sora against a horde of Nobodies. Axel ultimately met his end to that same horde of Nobodies. He extended all of his energy into one final "big bang," which took out every remaining Nobody, including himself. 
  
Before he completely faded back into the darkness, he confessed to Sora that he'd only kidnapped Kairi because he wanted to see Roxas again. He tells Sora to tell Kairi that he's sorry, and reveals where she's being held. He uses the last vestiges of his energy to open a portal for Sora. 
 
Axel was Organization XIII's Number Eight. His label was "The Flurry of Dancing Flames." He used two chakram weapons and employed the fire element in his attacks.  
 
In  Kingdom Hearts 258/2 Days he is confirmed to have another friend, Xion, who also befriends Roxas. When Xion is brainwashed to absorb Roxas, he doubts their friendship with her. His memories of Xion are erased by the end of the game.
 

Appearance

Like other Organization members, Axel wears the basic black gloves and boots. His black coat, however, is one of the more distinctive ones in the group, as its sleeves close up tightly around his arms. Axel himself is also easily distinguishable from other characters in terms of facial features, made easier by the fact that he rarely wears the hood of his coat up. Axel has a widow's peak, rather small eyebrows and thick, shoulder-length, bright red hair styled into slicked-back spikes. His eyes are a bright emerald color and he has a purple reverse-teardrop shaped marking under each eye. 

Personality

When Axel is first introduced at the beginning of Kingdom Hearts: Chain of Memories, he has a mysterious, stoic, and calm demeanor on par with that of Marluxia. A very good liar, he makes a point of keeping himself difficult to read, coming off as fooling around when really his mind is at work manipulating the other members around him. Axel often makes witty conversation with Larxene while Marluxia is away, though is almost completely unfazed by her flirtatious behavior towards him. He also has friendly bets with Zexion as to which member will be defeated next, seeming amused at their deaths. Eventually, Axel betrays both with no remorse. Vexen's cries for mercy only receive a cruel "Aren't you happy [to die]?" and a cocky "Goodbye" before Axel incinerates him without any hesitation. This cruel nature persists even when Marluxia uses Naminé as a human shield against him: Axel confidently declares he would eliminate Naminé to get to Marluxia. He is a person who does what is necessary to keep his actions, like those in Castle Oblivion, unnoticed by the rest of the Organization, so that his and his allies' goals are attained smoothly.

Axel's personality changes drastically in between  Kingdom Hearts: Chain of Memories  and Kingdom Hearts II  because of his friendship with Roxas and Xion. In Kingdom Hearts: 358/2 Days , he has a very sarcastic and laid-back, "go with the flow" outlook on many things, including missions and battles. He also is shown to have a very kind and protective side towards Roxas and Xion, which is ironic for a Nobody and his actions at Castle Oblivion. He acted like an older brother towards them, being their main source of advice and wisdom. In some cases he got them out of trouble even when it could and did  earn him his own trouble, like his dismissal and eventual betrayal of Saïx to protect them both. Axel apparently does not like to talk about his past despite Saïx's insistence on its significance. Whenever Roxas or Xion asked him about it, he would give a brief or vague answer, then try to change the subject, often avoiding eye-contact when lying.

At his death, he was at least able to recall how Roxas gave him a "bizarre illusion of humanity". An important thing to note is that in Kingdom Hearts II Final Mix, when Axel bids his final farewell to Roxas, it can be seen upon closer inspection that the teardrop at the end of the scene belongs to Axel, which clearly displays his unusual emotional capacity. Even during the events at Castle Oblivion, Axel displays emotion and acknowledges it when he begins laughing, but catches himself and stops. He even mocks his ability to feel during his death. Whether he, Roxas, Naminé, and Xion all seem have something unusual in common regarding the heart, is unknown. But it has been hinted by Xemnas, and Axel himself, that by being close in contact with Sora's heart, Axel began to feel emotions of his own.
 

Abilities

As the Flurry of Dancing Flames, Axel uses two uniquely shaped weapons called Chakrams, and specializes in Fire manipulation. He can summon pillars of flame at will and strike with rapid combos using his Chakrams. He can also surround his Chakrams in flame and throw them like boomerangs, spinning and looping them to hit opponents multiple times. In his one on one battle with Roxas in Kingdom Hearts II, Axel also summons a circle of fire to surround them and leaps into the flames to hide, emerging to strike with rapid attacks, and then leaping back to keep his opponents off their guard. Axel is a powerful member of the Organization, arguably even stronger, or at least a better fighter, than Saïx. This is seen when Saïx is defeated by Roxas, but Axel was able to defeat Xion at the Old Mansion, who at the time absorbed much of Roxas's power. However, Axel clearly put more effort into his battle, as he passed out after the fight, while Saïx remained conscious, though exhausted.

In Kingdom Hearts 358/2 Days, Axel has a Limit Break called Explosion. During Explosion, Axel throws his Chakrams at enemies while they're engulfed in fire, creating a small explosion of fire afterwards. While not being thrown, Axel's Chakrams spin rapidly, gathering fire. However, they can be thrown at any time, and do not need to charge.

During Axel's Final Limit, Axel combines his two flaming Chakrams into one enormous flaming Chakram, easily many times larger than the two Chakrams. The explosion after the attack is also much larger.
 

Weapon of Choice

Axel utilizes two Chakrams, named "Eternal Flames". Each Chakram is circular and red, with silver spikes and circles around the edges, and two black handles shaped like crosses in the middle. Each Chakram has eight spikes, possibly referencing Axel's rank in the Organization. Axel is very adept in the use of his weapon; he can throw them, use them as shields, or use them as melee weapons. He performs some unique attacks, including juggling them against an opponent, or throwing one across the entire battlefield continuously.

He also uses them in conjunction with his fire abilities, setting the tips, or even the whole thing, on fire before throwing them. From a scene in Kingdom Hearts Re:Chain of Memories, it is shown that he can set his Chakrams on fire from afar, acting as a remote detonator.

The Bond of Flame Keyblade, obtained from Axel, is similar in appearance to his Chakrams. Axel's Chakrams are among the few Organization XIII weapons that do not bear the Nobody symbol (the others being Xemnas's Ethereal Blades, and Roxas and Xion's Keyblades), but the spikes on the wheel do bear some similarities to the Nobody insignia.

In real life, chakrams are actually small razor-edged throwing disks used by warriors in ancient India. Axel's Chakrams bear more of a resemblance to Chinese wind-and-fire wheels, wheel-shaped weapons that are used strictly as melee weapons.