My wife and I have been not using soap for over a year. My hair is decidedly NOT greasy, nor is hers. We don't stink - though I do use a fragrance made from oils when I am working in my photographic studio - I get pretty exercised during sessions with kids - all the running back and forth is a work out, trust me!
I don't have any magical cured-me-from-cancer-and-a-bad-stepmother stories, it's just easier (less gear), and we don't smell like the detergent aisle at the grocery store.
We stopped because we wanted to reduce the overall load of crap that our bodies run into daily, and putting a LOT of stuff directly on your skin is a heck of a load overall.
The only soap I do use is when I shave using olive oil and then wash that off using some Bronner's soap, and a scrub with a washcloth.
And, yes I use soap to wash my hands all the time, though I absolutely DESPISE the smelly crap soap in most public restrooms. Yech! What DO they put in there?!
And, just to totally send many people over the edge, we eat raw eggs, raw milk, and meat from our friend's non-USDA ranch. Horrors! We'll die of everything!! :- )