Lets not be ridiculous now people. Recast.
The Joker is a character. If there was any other inarguable reason for Heath Ledger not being able to return, everyone would demand a recast.
The beauty of the Joker's character is that he re-invents himself all the time. It wouldn't be completely unreasonable (or heretical) for another actor to portray another take on the Joker in the next film - even if Heath was still alive. Remember that the Joker has gone to Arkham, he's had to spend months, possibly years in a straight jacket without his make-up (his real face) on. He will have been forced to undergo the structured society of establishment that he despises so much. His psychological condition will have changed - even if Heath was able to return to the role, it'd be a new spin on the character.
I really don't think it's respectful to Heath Ledger as an actor to take a character that he portrayed and lock it up for another 10-20 years because people are afraid to tread in his footsteps. Yes, its a landmark performance, but it isn't the only performance there shall ever be of the Joker from now on - that'd be ridiculous.
Heath Ledger was an artist. If he was alive now, he'd be proud of his work as an artist, because of his monumental contribution to the nature of on-screen villainy. I seriously doubt he'd be happy to know that by portraying the character to such an exceptional degree he effectively killed future portrayal. He clearly enjoyed playing that character - so why kill it just because he's dead?
The best way to honour Heath Ledger, in my opinion, would be to use his performance as inspiration to other great actors, to have other talented actors have a go at the same character he did - not with the intent to outdo him - not because he's dead and they want to move on and forget about him - but because it's a ****ing brilliant character that should be kept alive.
Heath Ledger enthused the Joker with an entirely new breath of life, why would he want that to end with his own tragic passing?
My only analogy would be your brother's favourite ever toy - the toy which he loved playing with and which he will always be remembered as having played with. Your brother gets hit by a bus. Should you, after mourning his loss, lock up that toy and never see it again? or, hell, play with it yourself because its a great toy.