In my mind, the Joker is the criminal representation of the Batman. However Batman is portrayed, Joker must be the vibrant ying to his yang or vice-versa.
For me, he's a conceited nihilist who thrives on the torment of others as a way of coping with the horrible trauma of his acid bath.
Ex: Batman used his tragedy to help people.
Joker used his as a gateway to vent his frustrations/wanton wrath
I really enjoy what Jack Nicholson did to establish the character as a formidable screen presence; I equally admire how Mark Hamill created a quintessential vocal for the Clown Prince, but I'm still hoping to see a man who's less . . . approachable. I don't want the audience to connect with the Joker on an amicable level. I want them to hate him, not because of the taxing morality of wrong and right, but for the reason that a small part of each viewer might crave the freedom that his insanity grants him. He's not bound by law, save that of his own direction. He has control that most people desire, but refuse to acquire or exploit.
Simply put, I envision his true essence as an inconsequential bastard who just does not give a **** about anything, anyone, or even himself; he's functioning or living, if you can call it that, solely for his own demented pleasure, and the rivalry(with others but specifically Batman) which attacks, befriends, and flourishes that pleasure, along with the self-ordained hubris of his lofty eyes. He craves acceptance in the form of adulation, and Gotham is pictorial of his kingdom, at least in the eyes of the 'would be' king.