I'm going to see the third Batman installment, The Dark Knight Rises, because of the action, the writing, the visuals, and just the overall quality that I've come to expect from the franchise. I'm also going to see it because of its implicit philosophical commitment; and its unspoken assumption about human beings, which is that they belong to a different realm of being that science cannot describe.
Before I elaborate on that point, it's worth distinguishing between a movie that explores a specific philosophical question in the course of the on-screen action and one that bases its entire world and the dramatis personae that come with it on the unfathomability of the human mind.
The Dark Knight does both and that's why it's worth distinguishing the two ways of involving philosophy in a storyline.
For example, the first two Batman movies both had important thought experiments in them. In the first Batman, there was a stylized version of the trolley problem. The trolley problem asks whether it's morally acceptable to divert a runaway trolley away from five people toward one other innocent person. Batman Begins contemplates that situation loosely in the final scene, involving the elevated train.
The second Batman also had a famous thought experiment in it, involving a prisoner's dilemma (was the ferry scene even a prisoner's dilemma?). In the ferry scene, the people on board are given the chance to blow up the opposing ferry (both have detonators) to save themselves. The temptation is not to "cooperate" -- meaning not blow the other party up -- and instead take the reward of survival.
However, the reason I like Batman goes beyond the specific thought experiments that are inserted into them, and the reason is that Batman is about the human mind. Batman is a detective of the highest order, and though he is agile and strong, he is first and foremost a tactician, always aware of what his enemies are doing. In fact, this is how, in the comics, he is able to defeat Superman, who he is often compared to.
This is part of the reason why people celebrate Batman as an "ordinary guy." He has no super powers, only his purpose and his willpower, and the intricacies of those terms are what is most heavily explored in the mythos of Batman.
Consider the fact that Batman's origin has early psychoanalytic themes etched all over it. He is rendered helpless by the killing of his parents and so, to master that traumatic event, embraces his other great fear --his fear of bats. He becomes the thing he hates, and that repressed fear threatens to come out at every turn. This theme is played out again and again by the cerebral, psychological nature of Batman's adversaries. Two-Face suffers a split-personality, Scarecrow is a sociopath who lives to instill fear in others, Bane is a sociopath, Dr. Szasz is a sociopath, and the Joker, the most archetypal of all Batman enemies is -- you guessed it -- a sociopath. In fact, there are numerous intimations in the comics and films that Batman is very similar to the Joker and that only a few things them -- one of them, Batman's utter refusal to kill which is a limit that the Joker tests at every turn.
Fear, drive, and the dark place that lives in us all are the watchwords of the Batman series, and they complement the Batman series so perfectly. But as philosophy knows, things like fear, justice, and willpower cannot be studied by science. Sure, science can study what happens to someone's heart rate when they are placed next to something they fear, and it can study whether such a person cries out, runs, or remains rooted in place out of terror, but it cannot investigate what it's like to be in fear; to live with it and to overcome it as Batman strives to do each day.
Batman is the ordinary hero and that phrase has deep significance, because every person has "supernatural" abilities that defy science, such as the ability to act from reasons, to will, and to fear. He is the hero that embraces these uniquely human abilities to overcome his foes, using fear, not invulnerability or laser vision, as his weapon. It is often thought that Superman is only vulnerable to Kryptonite, but that's not right. He is also vulnerable to going insane, or becoming depressed, or becoming a vegetable, and these weaknesses are what Batman exploits, and they are also the themes that the franchise explores so well.