I like to think of there being two kinds of situations where eye-contact is applied.
In friendly and familiar situations (flirting with a girl, talking with friends, chatting with a good acquaintance) I always maintain eye-contact, and find that the person on the other end gives it back. In these situations, you don't even notice that you are looking someone in the eyes.
The other situation type is serious-non-attached. Some examples of these would be when you're talking with a pastor, meeting new people, talking to your boss, or chewing someone out. Whenever you are in one of these, always remember that if you feel uncomfortable with eye-contact, odds are the other person will feel the same way (not always though, some people just always look you in the eye). In these cases, just look them straight in the eye. Make the first move! Force them to make the decision to meet your eyes or not!
And remember, being shy isn't a bad thing. A lot of girls/guys think it's cute when someone they start flirting with is a bit shy. :wink: