I agree with Mindovermatter on this. Some girls will look you in the eye and even maintain it when you are looking away. However, shy girls will rarely look you in the eyes because, like a lot of AFC males, they're afraid of letting their attraction be known.
As gav pointed out, emotion reflects most in a person's eyes, so if a person wants their feelings known, he/she will have no qualms about looking you in the eye. If they are shy, insecure, devious or dishonest, they will try to hide their eyes as though hiding their motives.
But, there are two very positive signs I'm aware of in terms of eye contact:
1. When you are facing a girl at eye level and she lowers her chin and gazes upwards at you, she sees you on a pedestal (guys do this too btw). Girls who do this, however, probably have quite deep feelings for you and won't maintain eye contact for long.
Of course, don't mistake this for her literally looking up at you if you are taller than her.
2. A VERY positive sign to look for is when a girl is talking or listening to somebody else and her eyes continually flick towards you. This can be considered her way of checking for your approval or trying to include you in her conversation.
I've never known these two signs to be wrong.