Of all the ways we communicate with people, eye contact is the most powerful. In his book, Eye To Eye: How People Interact, Dr. Peter Marsh says, "How we look at other people, meet their gaze and look away can make all the difference between an effective encounter and one that leads to embarrassment or even rejection." Whether it's a loving gaze, hostile stare, nervous glance or a refusal to look altogether, the duration of the contact (or lack thereof) reveals our interest in the other party and the situation.
According to Julius Fast in his book, Subtext, the "moral looking time" is different in different settings. With people we don't know where our personal "bubble of space" is also being invaded, eye contact hardly exists. In an elevator, on a plane or on the street, make contact if you wish, but break it immediately. Any glance longer than a brief one becomes a sign of recognition or rudeness. In general conversation, you can make eye contact for a few seconds at a time before breaking it. And in public speaking situations, glances of even longer duration are vital to getting your message across.