Batman's an IxxJ with matched T-F and N-S.
I think it's obvious that Batman's a natural Introvert.
The reason I say he's J is because he's very committed to closure and he's unbelievably disciplined... if he sees loose ends, he'll analyze the shit out of them and then tighten and knot 'em up.
I can't see him as straight S or straight N, because while he's a detective (that's his primary description... crime-fighting detective... not quite the typical 'superhero') and must pay exceedingly close attention to details and sensory input, he also relies heavily on his intuition and ability to think out of the box, to track down criminals and get himself out of tight fixes. If Batman weren't completely in control of his N, he would never have been able to defeat Superman.
T-F follows from the fact that he's a detective and he's often joked about as the brains of the Justice League, one of the smartest superheroes around, logically breaking down the world, people, and situations that need to be dealt with methodically. But he's also extremely passionate and driven by his emotion, his sense that the world is cruelly unjust. But it's not the abstracted NT sympathy... I believe Batman truly empathizes with other people. And no, I'm not saying Feelers can't be very smart people, but I think he's particularly T in his way of approaching the problems he regularly deals with in his work. Not to mention his ridiculous ability to utilize technology, which requires very strong T.
Batman's no-kill policy (which has rarely, if ever, been broken, and usually because it was absolutely unavoidable) provides a very interesting point of departure for MBTI and other personality classification attempts.
If I had to choose a single type, though, I'd go for INTJ.
____________________________
N.B. I'm obviously referring to Batman across his comic-book history with only secondary reliance on the films, though I think the Burton and Nolan flicks do a good job of capturing the darkness of his character.