Towards the end of the move The Dark Knight, the Batman throws the Joker off the top of a building. Then he saves the Joker. But why not just let the Joker die? He could say the Joker suicided. Or even if he assumes the responsibility of the death of the Joker, he can go into hiding. No one would blame him for killing such an evil like the Joker? 
There can’t be possibly any person more evil than the Joker, right?
It doesn’t matter whether anyone else blames him for killing the Joker.
He’d still know he did it.
DARK KNIGHT is based on comic book characters, but it’s not set in a comic book universe–by which I mean that Batman has no reason to think, at this point, that the Joker will periodically and endlessly break out of prison to go on new killing sprees. He, Batman, is entirely right not to commit murder here. It can’t be justified.
Because at the end of the day Batman doesn’t kill (except when he does)
Because he’s better than the Joker, who would kill him if the got the chance.
Did you miss the whole part of the movie about how The Joker wants Batman to kill him, and thereby corrupt him?
Batman doesn’t kill because he’d fall into the abyss and never return. Or at least, that’s the handwave they used in Under the Red Hood.
That character aspect of Batman was pretty well established in Rises, where Ra’s al Ghul almost taunts him during his climactic fight monologue. Batman responds that he won’t kill him, but he doesn’t have to save him. That’s as far as he’d go. The Joker’s death would have been out-and-out killing.
But what about a comic book universe, in which Batman does know that the Joker will escape, kill, get captured, escape again, over and over, until something is done about it?
Now, sure, in any kind of real world, the state would have executed him after the second or third episode. But what if they can’t? Batman is here to protect us by doing the things we can’t do. So much else of what he does is against the law. And so much else of what he does is blatantly immoral. He puts people in wheelchairs all the damn time.
At very least, if he’s going to play Vigilante games, he could round up twenty family members of Joker’s victims and let them decide. Hold a mock trial and then let them lynch the bastard.
Another trick would be to maneuver the police into a position to catch the Joker right in the act of murder, so they can use deadly force against him.
It’s not about the law, or morality. It’s about bargains. Batman has made bargains with himself about what he will and will not do. Most of us have done some variation on this–“If I do that I don’t really want to do, I will allow myself to do [Y] that I want to do later.” We do it to complete chores, to stay on diets, and many other things.
Batman does it to reassure himself that he’s still in control. His bargains draw clear lines, and it’s not really important to him that the lines are sort of arbitrary: “I can be a vigilante as long as I don’t kill anyone.” and “I can be a vigilante as long as I don’t use a gun.” He doesn’t spare the Joker because he wants to. He does it because it is, in his mind, a requirement for continuing his mission. If he breaks his bargain with himself, he’s supposed to hang up the cape, because he’s no longer in control. He’s become one of the monsters. Of course, it’s more likely that–like the rest of us–he would respond to the broken bargain by making a new one. “I can be a vigilante as long as I only kill murderers.”
He’s not standing over an abyss, as he imagines. He’s on a staircase, and he holds onto his precarious balance by not looking too hard at the step below…or all the ones he’s already taken above.
No the (movie) Joker doesn’t want to kill Batman. He wants to destroy Batman’s illusions, to show Batman that he’s a monster, just like the Joker is. He doesn’t get scared when Harvey Dent shoves a gun in his face, he’s delighted because he realizes that he’s destroyed him.
A dead Batman is just dead. A Batman that has to live the rest of his life knowing that he’s a monster is fun.
And note that, in the universe of the movie trilogy, Batman is entirely correct that the Joker isn’t likely to escape from Arkham Asylum by Tuesday and go on another killing spree. In the ten years between the second and third movie, the Joker hasn’t caused any problems.
It’s only in the comic books that the Joker escapes every time Batman catches him. Of course the comic books have sliding continuity, because otherwise Batman has been fighting the Joker since 1940. Bart Simpson was 10 years old in 1987, that would make him 37 today. But he’s not, he’s still 10. Same with Batman and the Joker. Either you accept that long-running comic books have to operate by their own logic, or you decide to put the characters to rest and stop caring about them.
I’m guessing that’s more a function of being forced to drop the Joker storyline altogether because of Heath Ledger. It’s hard to imagine they wouldn’t continue with the Joker for the third film had Ledger still been around.
(stolen and half-remembered from a jokey movie blog)
Joker: why don’t you just drop me and let me die, Batman?
Batman: I need you for the sequel.
Joker: Uhhh, yeah-- about that…
Precisely. Batman understands this, and knows that killing the Joker or even deliberately not saving him would hand him a victory – recall how he’d just mocked the Joker for the failure of his “social experiment”:
[QUOTE=Batman]
What were you trying to prove? That deep down, everyone’s as ugly as you? You’re alone!
[/QUOTE]
As for the comic-book universe where the Joker keeps stepping through Arkham’s revolving door to kill again, Batman’s refusal to kill out of principle and/or fear of becoming a monster as bad as the ones he fights have been addressed above. There’s still the question of all the other enemies the Joker has made, most of them with fewer such scruples.
Batman : Then why do you want to kill me?
Joker : HEHEHEEEHEHEE!!! I don’t want to kill you!! What would I do without you??!
====================================================
The Joker: Oh, you. You just couldn’t let me go, could you? This is what happens when an unstoppable force meets an immovable object. You truly are incorruptible, aren’t you? You won’t kill me out of some misplaced sense of self-righteousness. And I won’t kill you because you’re just too much fun. I think you and I are destined to do this forever.
Batman: You’ll be in a padded cell forever.
The Joker: Maybe we can share one. You know, they’ll be doubling up, the rate this city’s inhabitants are losing their minds.
Batman: This city just showed you that it’s full of people ready to believe in good.
Comic book Batman has a slightly more complex relationship with the Joker than his movie counterpart. Considering the huge body count that follows the Joker around, and the fact that the authorities have shown time and again they are completely unable to keep him up locked up, there is no moral justification to not kill the Joker any more.
You could argue that Batman doesn’t want to be an executioner, but he has also gone out of his way many times to save the Joker’s life, often risking his own to do so. Once, the Punisher turned up in Gotham, and was seconds away from shooting the Joker, but Batman intervened and stopped him. He only had to wait for another 5 seconds, and countless lives would have been saved, but he just couldn’t let that happen.
http://www.ferretpress.com/weblog/uploaded_images/pb1-727155.jpg
The reason for this is because Batman is as psychologically damaged as the Joker. He grew up isolated in his huge house and was denied the attention of his parents from a young age. He claims the Joker acts without reason, but that isn’t true. The Joker is obsessed with the Batman. Every single thing the Joker does is to attract Batman’s attention. Subconsciously, the Batman revels in that obsession. The Joker’s infactuation with him is the closest thing to parental love that the Batman has ever felt
As far as sequels go, it was transparently obvious to me that the “judge” of the citizen trials was supposed to be Heath Ledger’s Joker. Cillian Murphy did an admirable stand-in, but he was clearly channeling Joker’s giddy strangeness rather than Scarecrow’s intensity.
There are a number of parallels between the Joker and Batman. Sure, you see Batman as the good guy and the Joker as the bad guy, but a number of Gotham’s citizens are almost as afraid of Batman as they are the villians (this has always been somewhat downplayed in the movies), and that’s something that Batman struggles with. In that universe, the Joker would surely kill Batman if their positions were reversed. Therefore, in Batman’s mind, NOT killing the Joker is one of the few important things that distinguish them from each other.
Remember that Batman has a strict policy of “no guns”.
Which I suppose doesn’t count the rockets and autocannons on his Batmobile, Bat Bike, and Bat Wing VTOL gunship.
So maybe he means “no guns smaller than 20mm”
Also, movie Batman specifically made a point in the first film that while he won’t kill anyone, he doesn’t “have” to save them either.
In the Dark Knight Returns an older Bruce Wayne does take himself to task, blaming himself for all the people he’s killed by allowing the Joker to live. He and the Joker obliquely acknowledge that it’s the chief way the Joker tortures him, knowing that’s the sole reason for most of the deaths.