It also goes to why pick up artists, or pick up scenes in movies, always start with eye contact. Personally, if someone catches me looking at them, I always pretend to be looking at something right beside them or shift my attention away. You don't always want a special feeling when looking at a stranger, I guess it's how outgoing you are.
Other, unrelated studies have looked at people's behavior when even the image of eyes is around. A poster of someone's eyes staring at you, for instance, will inhibit people from stealing at a newsstand. The theory here is that we feel as if we're being watched, which stimulates our own internal cop (we watch ourselves; without the eyes there, we basically ignore ourselves, it would seem), but perhaps we just get self-aware when faced with the prospect of a special feeling.
Grocers take note.