One that pops to mind for me is Francis York Morgan, an FBI agent, and the main character of the "horror" game Deadly Premonition.
He's an eccentric, but nice, character who has an imaginary friend he talks to named Zach who helps him solve crimes.
He seemingly only solves serial murders and not assassinating leftist leaders...as far as we know..
Robocop
I'm still a little angry that they never did manage to get that secret prime directive out of his programming so he could go full-on murder-machine against OCP