So, what happens with The Dark Knight? While I don't expect Christopher Nolan or Christian Bale to comment anytime soon regarding this as people in the media would think they are only thinking about the Box Office dollars, but it is something of an important question.
Now, we all know that roles can be recast and in fact they already have in this current incarnation of the Batman franchise. With Maggie Gyllenhaal replacing Katie Holmes as Rachel Dawes, we know that Nolan is afraid replace someone. But let's be honest. That character is small compared to The Joker in the Batman universe. The Joker is the king of all villains, the one who drives Batman the most insane. The one who is always a thorn in his side. And I'm sure that Nolan knows this. I haven't read the script and I probably won't since I don't want the movie to be ruined for me before I see it on the big screen, but you would have to imagine that for Nolan's telling, the Joker doesn't die in this one. Nor should. And the movie is in post-production, so it's pretty much finished except for re-takes that might be needed to fix somethings. I hope the ending isn't one of them.
To me, you leave it end the way it was supposed to. I know that if they left it open-ended, then the question would be, is the Joker going to be in third one? And I imagine that Nolan has an idea of where he wants to go with the third one and right now only he and his brother, who co-wrote Batman Begins and The Dark Knight know how they want the story to progress. And if that includes the Joker, then maybe they will have to re-cast the role. But for now, The Dark Knight should be left alone and keep the ending that they filmed. I'm sure if someone were to ask Ledger by chance, he would have wanted it that way.