I'm not sure what most countries will refuse entry with, apart from the obvious. I know that you are refused entry to the USA if you have any driving related offences and several countries will refuse entry to violent crime offenders, but asides from those i'm stumped.
Can you be turned away from America for running a red light?
Technically, any criminal record excludes you from the visa waiver program and you must apply to the embassy for entry. The definition of criminal record normally excludes minor traffic offences dealt with by means of a fixed penalty notice, but I'd check if you're concerned.
A US immigration guy once asked me if I'd ever been in trouble with the police and wouldn't take 'no' for an answer. Obviously, I look shifty.
Aww, you should have said, "Buddy, I AM the police!".