I'm not into the whole "natural horsemanship" thing, but almost every afternoon I go out and sit with my horses, mostly cause I have nothing better to do. They all come up, beg for some attention, and move on.
When I was working with untouched horses, I would get them into a pen with a stock waterer and a cement pad built up to the waterer and sit on the cement. Normally, the horse would stand as far away from me as possible and stretch their necks as far as possible to get a drink. I would also have a pile of hay sitting by my feet. And I'd just sit there for the afternoon, and talk to them, make noise, walk around, just do stuff around them. It helped in getting them less afraid of you.
I still wouldnt call it natural horsemanship.