From what I've heard, you can run down the street and punch random people in the face, shoot anyone you want except maybe kids, hit anybody with your car. You can hack ATM Machines and steal money. Pretty much just chaos in the streets if you really wanted to.

And the cops don't really give a damn, unless you're just tearing up the city and causing an extreme level of mayhem. You'll mostly have to worry about local gangs if you're acting up in their territories.

Essential story NPC's will not be killable, though.