When an educated English Speaker intends to say "Would HAVE", they instead contract the written form to would've. Less intellectual people (read: Dumbasses) then read this and, unable to grasp the concept of abbreviation, pronounce it as "Would've". This, due to laziness, was then mutated to "Would of," whereupon Bahamut was returned to mortal flesh and mankind entered a new age of darkness, suffering and general illiteracy.
"I would of kept talking, but she asked me if I wanted to of sex."
"Would HAVE. You've doomed us to an age of darkness, suffering and general illiteracy!"
"Why don't you of a short walk off a long pier you Grammar Nazi."