My own headcanon is the Joker has been killed multiple times but not by Batman, at least not deliberately. The Joker has a small army of imposters, dopplegangers, clown henchmen, and back-ups who are actually as much the Joker as the Joker himself. They adopt his identity, carry out his plans, and often commit various clown-themed crimes on a lesser scale than the Clown Prince himself devises just to keep "his" name in the papers.
Jack Napier (for lack of a better name) has escaped three times in the history of Gotham City and some of them have been for lengthy periods but there's something like sixty Jokers locked up in Blackgate prison or who have gotten themselves killed fighting the Batman, blowing themselves up, or getting gunned down by the police who do not hesitate to do so when Batman isn't directly handing them over in batcuffs.
The mad-dog killer and psychopath Jokers are not the actual Joker-Joker as while Joker is a mass murderer, he has one simple rule:
1. It has to be funny.
Which wearing your own face isn't.
Harley has, notably, dated six of the Joker Clan.
Tim Drake has mentioned this makes Joker a Stand Alone Complex but Batman, surprisingly, doesn't watch anime.
