Many people advocate a 21' or so "bubble" in which you do not allow an approaching aggressor to enter if in a confrontation. The reasoning is that 21' is about as far as an attacker can run at an "average" speed and still give you time to draw and engage him.
Take a look at the following video on YouTube and come on back when your done (embedding was removed upon request - guy was probably tired of being lampooned on various other web sites)
21 Foot Rule Less Talk and More action (compiled and shortened) - Youtube
Now take a look at this video (that I have posted in the past)...
...get the idea now?
Your bubble may vary slightly or to a great degree depending upon your training level. The best rule of thumb is to always be vigilant of your surroundings and ready to react to any threats immediately. Even in the second video if the shooter was distracted by a question when the exercise started, he still knew that the "attack" was imminent. Therefore his brain was already prepping itself for action by working out the scenario before hand and his muscles groups were already receiving impulses prior to the target starting. When you encounter danger "in the wild" you will often face it with out any warning. This is where training pays off.
2nd Amendment to the Constitution of The United States of America
A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed.
"I ask sir, what is the militia? It is the whole people except for a few politicians."
- George Mason (father of the Bill of Rights and The Virginia Declaration of Rights)