Actually, Joker does not die at all. In Under the Red Hood, after Batman rescues Jason from the bomb going off, the Joker is then returned to Arkham Asylum. You may be thinking about the movie Batman:Return of the Joker, where Tim Drake shoots him.
Joker never did die in the batman comics.
Yes he did die sadly.
In a perfect world.
yes he spontaniously combusted
Batman didnt kill the joker because of his rule. His rule is to never actually kill anyone. So joker's mission was to make Harvey dent fall. That worked with Harvey dent. (He became 2-face.) The joker WANTED batman to kill him so that batman can break his rule. And also batman didnt kill harvey dent, they both fell off the ledge. Batmans armour protected him but Harvey struggled a little then died. Gordon said that the joker won harvey had become evil, the white knight had fallen. So Batman said that he can never let the joker win. He can never let people's hope fall so he took the blame for Harvey's crimes and no one ever knew that harvey was evil. So therefore batman won, but joker was extremely close to winning.
If you are talking about Batman Arkham City then yes. If you're talking about Batman Arkham Asylum, then no.
It can be assumed that he did not die at the end of "Under the Red Hood" although not directly shown him surviving the explosion Batman and Joker both survived and Jason was right next to Batman at the time of the explosion, DC also went on to write a comic series with Jason as the Red Hood as the anti-hero, so one can assume he survived.
Many times (In the movies and TV shows) Batman has threatened to kill The Joker. He has never carried out his threats because it would violate his conscience. There are many comics where Joker does die and I believe there is an alternative comic called 'The nail' where Batman kills The Joker.
Jason surives, but is no where to be found after the explosion.
yes he is shot bye joker in the sholder. no he did NOT die.
yea. jokers dies in the end. Depressing
No, he dies in a flashback of the Batman Beyond movie, which while in canon with the batman animated series, isn't actually part of it.