A little fear is good. It makes you more alert and can give you the boost of energy you need to deal with a crisis situation. But at times fear becomes overwhelming and debilitating. In the extreme case, it can become a phobia. Some people are afraid of other people and have a social phobia or social anxiety disorder (SAD).
Fear is a built in response mechanism that has helped us survive as a species. Most animals also have that fight-or-flight mechanism, but it doesn't always work in their favor. Driving down the street the other day, a squirrel in the middle of the road became so confused, it ran right in front of my car when it could have simply strolled to the side of the street -- or even just stayed where it was and it would have been safe. But it became overwhelmed with fear and had an irrational reaction. Fortunately, I was going fairly slow and was able to stop in time.
We sometimes create our own crisis situations. If we'd only talk a calm approach and understand the situation before reacting, we'd recognize that there is no danger. Like the squirrel who overreacts to the approaching vehicle, we overreact to stimuli. It can become an autonomic response if we're afraid for an extended period of time. If you grew up in a household where you didn't feel safe, you may look at the world as a dangerous place and you see danger where there may be none until we create it.
Fear is a powerful emotion. 9/11 brought out the fear in many people. Fear affects people ability to think clearly. The response by our government to 9/11 caused far more suffering and damage to our country than the attack on the World Trade Center. Most religions play off people's fears -- mainly the fear of what will happen to us when we die.
In Buddhism, fear is what we are trying to overcome to achieve peace in our lifetime. In most cases, fear is unnecessary if we develop an understanding of the situation. Right Understanding (or Right View) is one element of the Noble Eightfold Path -- one of the "wisdom" elements.