You guys, what the hell is wrong with you? Axel didn't get rid of the entire Organization; only the traitoris (is that even a word?!) ones. In CoM, though it's not put out in the open, the Superior (whomever that is...I'm going with DiZ) guessed that Marluxia was going to try and take over the Organization. So, he sends Axel to see what's really up. When Marluxia tells Axel to "eliminate the traitors" (or something to that degree when he's speaking of destroying Vexen), Axel sees this as his cue to eliminate Marluxia and Co. Now, there are a lot of people saying, "He didn't have to kill Vexen, or Zexion." Yes he did. Vexen was sort of a traitor to the Superior to begin with. He knew of Marluxia's plans and, if they were applicable, would join him. Is that not being a traitor? Also, Zexion was in Castle Oblivion with Marluxia and Co., most likely doing the same thing as Vexen; observing his plans and seeing whether they could be done or not. Axel did the Organization a favour in keeping it alive by killing off some of the traitors.
Now what, let's get back on topic. I think Axel is neutral as well: both "good" and "bad." However, I think he's slightly more evil than not. Why? Because I'm not too sure if the Organization's intentions are for the better good. Almost every picture we see them in they're up to no good, weather it's Xaldin practically mugging Belle, an Unknown influencing Beast to attack Sora, Sora attacking an Unknonw or two, and Axel facing off against the BHK. Even the BHK whips out his Keyblade in an attempt to charge DiZ, to no avail. Of course, they're only snapshots of the big picture that is KH II.
That's not to say Axel may have some "good" in him and have an agenda of his own. He has the personality of one who is looking out for himself and does things because they're fun, may amuse him, or just for the hell of it. This Organization member is definately a wild card. But, I will close with this: in the TGS trailer, with the BHK and Axel facing off, the look Axel gives the BHK as he summons his Wind and Fire wheels is of one saying "I will kill you, and I will thoroughly enjoy it."
Thank you for your time.