Gregg... I'm gonna kill you.
Just words or a real threat ?
Over the internet they might mean very little however, face to face, if you considered my intent be real, then you'd be within your rights here in the UK to physically defend yourself, even though to that point, you haven't be physically assaulted.
Walking way in those circumstances just might not be the right thing to do if the person issuing the threat actually means what he/she says.
Wow...in the US I don't think this is the case. I can talk all kinds of trash and make all kinds of threats but unless I take steps to actually make it happen, no verbal threat that I'm aware of can be regarded as an attack warranting violent response. Of course there are special circumstances such as airports etc. but so far as I am aware, between two people in most locations, responding with aggressive physical action to verbal action is a crime. There isn't always a clear line between the kinds of physical action which warrant physical response, but words alone should never provoke physical retaliation.
I agree simply walking away might not be a safe option...or at least, turning your back or otherwise allowing yourself to be in a compromised situation defensively could open things up for serious injury. I've seen too many sucker punches to think otherwise.