Batman an INTJ? ISTP? Nyuh-uh and definitely not.
First off, I want to say that I'm talking about the Christopher Nolan films in this post. Batman from the comics may be a different personality type, but I definitely think he's an INFJ in the movies. Then again, people are probably going to assume that I'm just saying that because I'm biased, so I'll have to support this. Let me just say that I've actually seen the movies, both of them. Multiple times. Hopefully that gives me a bit of credibility.
Anyone who thinks Batman is an ISTP is probably just looking at the surface and barely spent any time actually taking a good look at the character. He's not an ISTP. One could probably stereotype any superhero as an ISTP without knowing anything about them. ISTP's are adventurous spirits who do heroic things for enjoyment, but that isn't Bruce Wayne. He's driven by a need to help Gotham- he isn't driving big cars and jumping off buildings for the heck of it. They touched on this in The Dark Knight when Bruce was getting tired of being Batman. As Harvey Dent said, "Whoever the Batman is, he he doesn't want to do this for the rest of his life. How could he?" (The quote was something like that). Bruce never gave any explicit confirmation of that, but you could tell that it was how he felt from the look he was giving Harvey at the dinner table. He wasn't enjoying his job as Batman and he wasn't getting any adventurous kick out of it. He wanted a more normal life, not an ISTP 'life on the edge'. Bruce was ready to easily give up his role as Batman because he felt it was the moral thing to do- an ISTP wouldn't have let go as easily as Bruce did and accepted a life behind bars. True, that didn't happen, but the point is that Bruce was ready to make it happen.
INTJ makes a bit more sense when you're typing Bruce/Batman, but I disagree with that, too. One of the major themes in the movie was Bruce's 'limit' or 'weakness' in that he couldn't always do the practical thing and let his emotions get in the way at times. He thought with his heart. That's an INFJ weakness and it's not something that INTJ's tend to let bother them. When Bruce was getting ready to turn himself in to stop The Joker from killing people, he knew it wasn't the practical thing to do. He knew that turning himself in wouldn't stop The Joker from killing people. Instead, Bruce said "I see now what I would have to become to stop men like him." He didn't want to become that person. It would've been the practical, INTJ thing to do if he had chosen to become that person, but Bruce wouldn't be able to live with himself if he violated his INFJ moral system. Remember how Batman refused to let the Joker die in their last scene together? Once again, it was another INFJ-driven decision. The practical, INTJ thing to do would've been to let The Joker die. Some might argue that Batman kept the Joker alive because it would be impractical to let the public see him do that, but the fact that he was willing to take the blame for the killings at the end of the film completely contradicts that. Batman couldn't let The Joker die though, because it would've been a violation of his moral code if he did. He acted the same way any INFJ would in their need to stay true to themselves.
So... Bruce Wayne strikes me as an INFJ. He is a "champion of the oppressed and downtrodden" Gotham City first and foremost. He isn't someone looking for kicks and adventure (INTP) and he isn't doing things in a detached, analytical way (INTJ). He does what he does because he believes in it so strongly. If anyone watched Batman Begins, they'll know how personal everything was to Bruce and how passionate he was about his work. He went on an emotional journey in that first film. INFJ's and ENFJ's are really the only types that I can see deliberately getting themselves in prison just because they hate criminals. The will to do those kinds of things takes a certain kind of emotional attachment to an idea that screams 'INFJ' loud and clear to me. Bruce's affinity for logic and science doesn't disqualify him from being an INFJ, though many of you may think that it does. INFJ's are known to be just as good as INTJ's at sciences, even though they tend to gravitate to other things. INFJ's do things just as systematically as INTJ's do, the difference between the two is that INFJ's have a special kind of personal drive to do those things. Bruce was born with all the tools he needed to be a 'detective superhero,' but that came with being an INFJ in his case, just as well as it may have come for an INTJ.
Batman/Bruce Wayne is an idealist who does things out of intense devotion, both to Gotham City and to his morals. That's what drives him and that's what makes him an INFJ in my eyes.