There've been a few, VERY few, people whom I immediately found it easy to talk to while maintaining eye contact. Really just those I have spirit connections with -- I guess because we already have that sense of intimacy. Strangely, if I'm crushing on someone I tend to REALLY avoid eye contact because the longer I maintain it the more impossible it is for me to think about anything other than kissing and touching. It's easier if I have no romantic interest or if there are clear boundaries (like with a co-worker). Or if there is already intimacy there, because then I don't feel compelled to close the distance between us now-now-NOW!
I need prolonged eye contact like I need touch or communication. For me it IS a kind of touch, spirit touching spirit, and it is a kind of communication too, spirit speaking to spirit. At the last cuddle party I went to, we did an eye contact meditation which was INCREDIBLY profound for me, even more so than the actual cuddling was. The downside of this is if someone usually breaks eye contact quickly I feel shut out and rejected, like I would if they shook off my touch.
Oh, and another aspect of this is that I loathe glasses because they break that contact. Even though aesthetically they appeal to me, I really don't like for people to wear them -- like holding hands through gloves, it's just not the same.
How does eye contact affect you? I've never talked about this with anyone before ('cause this is a recent realization) and I'm curious.