Something else came up while I was reading various articles about Batman. Grant Morrison said in an interview that
Batman kills the Joker at the end of the Killing Joke. I never really thought about it that way: I always saw the book as implying that they were doomed to go at each other forever. But when I look at the book through Morrison's eyes, it now seems much more logical to me that Batman does in fact kill the Joker.
Obviously, that act isn't in continuity because the Joker shows up after the Killing Joke. And the script doesn't say "Batman kills the Joker" (you can actually read the script
here). But Brian Bolland (the artist) seems to imply that it is supposed to be ambiguous what happens in the end, and it can only be ambiguous if one of the possible endings he was thinking about was that Batman does kill the Joker.
Also, Batman himself basically says that this event is their last chance to avoid what he sees as a death spiral where eventually one of them will have to kill the other.
But what sells the idea to me is the Joke. For those who don't remember, this is the joke the Joker tells at the end:
Its not actually a very funny joke, really. But it makes Batman laugh hysterically. I think that's because the joke is about them. Batman and the Joker are both trapped in the asylum. Batman manages to jump across the roof and escapes the prison of insanity. The Joker is afraid to make the leap. So the Batman extends a hand to him, as he does in the Killing Joke. The Joker sees the offer like the first man shining the light across the way - its a totally ridiculous offer. But the punch line is that the Joker doesn't see the offer as ridiculous, rather he's so far gone he doesn't see the offer as crazy, he's afraid it will actually work just well enough for Batman to hurt him even more by revoking the help.
The joke is that Batman offering to help the Joker is exactly like two crazy people debating whether or not one will turn off a flashlight half way. Batman is trying to convince the Joker he won't turn off the flashlight, when any sane person would see that's besides the point. In other words, they are doomed.
When Batman realizes this, he laughs. But then, if Batman realizes that the Joker is genuinely hopeless, that all along he's been offering a flashlight to a crazy person, his belief that there is an option besides killing the Joker has to end. And that's when he kills him, which is why the laughter suddenly ends.
It is certainly not the only interpretation of what happens at the end. But I think it is a viable one.