What a great character. Of all the super heroes created in the last 100 years, Batman is definitely the most intriguing. There are tons of other comic book superhero characters out there, some have more interesting premises and themes like the Wolverine, Hellboy, Spawn. Even lesser known characters from Batman's same publishing company (DC) on the surface have potential to be more interesting like Firestorm, Animal Man, Swamp Thing, Doctor Midnite, and Deadman. However, Batman towers above everyone else in popularity in the comics universe, and in pop culture. The fact that until recently, Batman (Bruce Wayne) was one of the few DC heroes from the Golden Age (1938-1950) to not die or retire and be replaced by another younger character attests to his popularity and staying power. Boom Tron made him their Badass of the Week in July.
Batman's origin has been told by numerous writers in numerous mediums. Not only is Batman printed monthly in several comic titles, but he has also been the subject of 2 movie serials, a live action television show, 5 animated television shows, 5 animated films, 7 live action films, and 28 video games. Basically, a boy born into privilege has a traumatic experience when his parents are gunned down in front of him. Instead of spending decades in therapy, and for the rest of his life trying to recapture a ruined childhood, Bruce Wayne devotes himself to becoming the best crime fighter ever.
A Christian interpretation may be that Batman views all life, even the depraved, criminal, sociopathic kind of life to be sacred and redeemable. But I'd like to think that Batman would much rather toe the line at murder rather than cross over into the world of the very things he fights. Keep this idea in mind for later.
Bruce Wayne decides though, that it isn't enough to just bring criminals to justice. The police do that everyday. Striking terror into the hearts of villains while bringing them to justice is way more effective. And so, he dresses up like a bat, which is a pretty scary animal. The fact that a grown man dresses up like a flying rodent doesn't seem to bother anyone, the other traits mentioned above make his wardrobe less silly.
On top of all this, unlike his peers Superman, and the Green Lantern who also uphold law, order, and justice, Batman has no superpowers or magical energy paraphernalia. He is just a man, a man with more wealth than some small countries, a good education, and the gift of being a good detective.
Great heroes are often complimented by great villains. This very idea is often a central theme for the Joker, perhaps the greatest comic book villain of all time. Batman's villains do not stop with the Joker, however. The Batman villains have the potential to be the most depraved, insane, dark, and twisted villains ever conceived. Even the more goofy villains created during the campy Silver Age like Mr Freeze, Poison Ivy and Calender Man have been written in ways that reveal how disturbing obsession can become.
These guys are not like Spiderman's mostly animal themed villains, or Hellboy's fairytale monsters, or even Superman's mostly super powered Earth threatening alien adversaries (this doesn't count Luthor, in fact, he would make a great Batman villain). Batman fights not just criminals, but fractured human psyche at its worst. These villains are not cliche cookie-cutter hero opposites bent on doing bad things for badness sake, they come largely from places of virtue... virtue gone insane. Plain crazy people are bad enough, but most of these Batman villains are also very intelligent. These are the insane scientists, professors, and doctors.
Among the long list of villains, Batman faces a variety of: deranged psychologists (Hugo Strange, Harley Quinn, Scarecrow), twisted scientists (Mr. Freeze, Poison Ivy, ManBat, Blockbuster), evil doctors (Hush, Professor Pyg), terrorists (Ra's Al Ghul, Bane), mobsters (The Falcones, Scarface, Black Mask, Maxie Zuess, the Penguin), thieves (Catman, Catwoman, Cluemaster), a district attorney (Two-Face) and egomaniacal fanatics (Mad Hatter, the Riddler, Calendar Man)...
and this guy...
the Joker, who often fits into all of those categories. The Joker has become the most well known Batman villain. All heroes have at least one well known anti-thesis. Superman has Lex Luthor, Spider man has the Green Goblin, Sherlock Holmes has James Moriarty, James Bond has Ernst Blofeld, and Batman has the Joker. The Joker makes much of this relationship with Batman. The Joker has passed on killing Batman when given the chance, his explanation being what would the Joker be without a Batman? The Joker seems to be his own study in madness. However, recently in the mythos, it has been established that the Joker may not be insane after all, which makes his character all the more intriguing and evil.
As suggested above, Batman has embodied fairness, and justice, which are virtues. Batman battles what happens to virtues twisted by madness. There is a line somewhere that these villains have crossed, and Batman continues to refuse to go there, keeping his own madness at bay.