An interesting experiment to try is to spend one day walking around making eye contact with everyone who passes by, and another walking around not making eye contact with people.

In my experience, my day always ends up being better when I'm making eye contact. Not only do I not bump into people (because I can tell where they are going), generally you get better responses from people, as they see you as being more approachable/honest/etc. People remember you.

On the flip side, if you have a desire to be invisible, walk around not making eye contact. Hardly anyone will remember who you are.

That's purely anecdotal, but try it for yourself.