I remember, when the teaser trailer came out, and all Joker said was, "Starting tonight, people WILL die. *breath* I'm a man of my woooord. HEEHEHEHAHAHAHAH"
My first thought, I remember this so clear; it was a Columbo moment, I put my hand to my forehead (but my first two fingers don't touch my forehead due to the imaginary cigar) and went, "So this is what a post-John Doe Joker is like!"
It made perfect sense. With the exception of the bizarre Rastafarian Joker in The Batman cartoon, the Joker's last reinvent was Mark Hamill's in Batman: TAS - which was '92. Three years before SEVEN.
So, come 2008, and Nolan wants to make a proper, terrifying psycopath, and John Doe, the psychotic with no past, no 'reason', no identity, is their, lurking around in the cultural memory.
As for Alex from Clockwork, I can definitely see how that was not only an inspiration, but a brilliant place to draw ideas from. It's very much Alex + John Doe = Joker.
John Doe + Terminator = Anton Chigurh.
I am so geeking out about movies right now. Dark Knight, Seven, Terminator... that would be a great way to spend the next six hours instead of sleeping.