I've heard Batman be typed as INFJ, ESTJ, and then people go so far as to say he's INFP!
He's probably ENTP. He's an inventor vigilante, not interested in fitting into society--he's sort of detached, yet not isolated. At the same time, he still gets around, goes to socialite functions, etc. but isn't there to fit in and be a part of something. He's got his own ways.
Now, I pose the question: Do you think Bruce Wayne is typed differently?
I always had him pegged as a INFJ. Why? Because regardless of his methods, the heart of his character is
justice. He doesn't kill criminals because he believes in the rehabilitation system. After all, we all know that Arkham Asylum has a revolving door, but Batsy is relentless in shepherding them back in there. I think any other type would have eventually say, "Oh f--k it," and recall their strict, no-gun policy and blow the Joker's head off. Hm, that already sounds a bit idealistic to me.
Also, his sense of justice has him alienating himself from people. He's self-sacrificing, guided by the notion that 'there's nobody else that can do this but me.' And aren't INFJ's a little famous for their relationship issues when they're hell-bent on something? When they don't want to get people hurt, they'll withdraw into themselves.
Yes, he is an inventor and he has a play-boy persona by day, but these can be explained away by INFJ type as well. INFJ's are social chameleons. We are whatever we need to be to other people, regardless of our inner discomfort and beliefs. Batman is the identity; Bruce Wayne is the persona.
Furthermore, INFJ intelligence and intuitive capacity, while it draws them to more right brain pursuits initially, does not bar them from persuing the sciences, as they are fully able to grasp the abstract. A highly developed 'J' function can ultimately govern what is practical and what is needed to fulfill the goal of 'the greater good." Meanwhile, this sense of 'the greater good' is something I perceive to be more developed in an 'F' type than in a 'T'.
So I say Batman is an INFJ because at the core of his character, there is Justice, Vigilantism, Fairness. The catalyst that propelled him into where he is now IS feeling, an inner sense of right and wrong, and the desire to do good, not for the sake of glory, but because he knows he must.
That's the crusader, champion of the down-trodden, paladin sense that defines what it means to be INFJ to me.