As far as Batman goes, arguments can be made based on two clauses in the PHB that describe his behavior.
LG: "[He] combines a commitment to oppose evil with the discipline to fight relentlessly."
-Perfect description of Batman, however...
NG: "He is devoted to helping others. He works with kings and magistrates (e.g. JLA/Commissioner Gordon), but does not feel beholden to them."
-Clearly, this describes the Dark Knight, as well.
Ergo, the only conclusion one might draw is that he does not fit the DND alignment system perfectly, as previously observed. However, I would personally classify him as an extraordinarially dedicated Neutral Good individual.
As for his class levels, using the current Batman as a mold, he most assuredly enters the Epic levels. As a member of the JLA, composed mainly of Demi-Deity level characters (in my opinion), one must certainly be at a high level to sit at the "round table."
Thus, I would most likely argue for a build similar to Monk 10/Rogue 20. His fighting prowess matched only by a few characters in the DC Universe, and most other comic book universes. His mastery of the stealthy arts, in addition to his vast knowledge of a wide variety of subjects, necessitates a tremendous dedication to the Rogue class, with possible arguments for classes such as the Shadowdancer or Thief-Acrobat (though I feel pure Rogue is most appropriate). Interestingly enough, if one were to go with a LG take on the Batman, his dedication to justice and personal conviction, as well as sense of self, might necesitate 2 to 3 levels of Paladin. To be sure, Batman can indeed "Smite Evil." Further, increases to saves, (self) healing w/ lay on hands and immunity to fear can represent his juggurnaut-like perseverence, his recouperative powers (I mean, his back was broken!) and his unwavering cool.
Since I simply do not wish to write up all his skills, I will end with my opinions on his abilities.
Strength: 18
-Quite simply, this is as strong as humans can be. Batman, through force of will or raw muscle, is a paradigm for humanity. Ergo, his strength is the maximum for humans.
Dexterity: 18
-I would place Grayson, as the best acrobat in the DC universe, as possibly above the "peak" established by DND. Really, Batman dodges everything. He throws Batarangs with uncanny precision. Basically, place him 1-2 pts below Grayson, wherever you think that might be.
Constitution: 20
-Batman's been stabbed, burned, drowned, broken, poisoned, shot, and even temporarially killed (heart restarted). He doesn't die. Plain and simple. His constitution is, like many comic book characters, above human. Like the proverbial cockroach, Wayne's indomitable will will ensure he lives for a long, long time.
Intelligence: 18-20
-This one's tougher. Batman's IQ was reported by writers to be around 200. That's pretty freakishly high. However, depending how you convert IQs to Int, if you do at all, this one's a little subjective. I would tend to go for 20, but that's just me. There is very, very little he does not know.
Wisdom: 18
-Indomitable will, incredible leaps of intution. I would put this higher, but I am of the persuasion that Batman should have above 20's for most mental abilities. Don't want to get flamed for that
Charisma: 20's
-Scary. No one screws w/ Batman. Plus, when it comes to sense of self, Batman's got it down. Highest Charisma in DC universe, bar none, I would have to say.
Hope someone finds my rambling interesting. Please, comments and criticism welcome.
Cheers,
Billiarmus