I avoid direct eye contact as an ordinary habit, but at the same time I use it fairly often, perhaps frequently even. Yet when I do, it's always intentional. I use it only very briefly, never sustaining it for too long, as a means of making authentic connection. Most of the time what I hope to express is a sincere interest in that person and kindness. Eye contact can cut through the superficial norm of polite dialogue.
For example, if I'm at the check-out register or over the counter at some food joint, as I leave I may look the person directly in the eyes, slightly smile, and say "Thank you" or "See you later" or "Have a good one" etc. Yet I don't make direct eye contact with everyone, I almost intuitively discern to whom and when it may be something that is appropriate (well received) and maybe even needed. I'll be sure to make eye contact here and there if I'm in a personal conversation that is sensitive, depending on the context.
That been said, making direct eye contact can be a little scary, it makes one vulnerable, and I don't think it is something to lightly throw around, nor something that has to be entirely reserved for a few intimates. When I've used it with strangers in a discernibly appropriate contexts, and in the appropriate way, there is something profound about those little encounters. Sure, they're a stranger in one way, and that comes with certain valid boundaries, but we're all kindred folk, and it's a wonderful thing when through the window of the eyes the souls of two strangers meet.