For the first month, my skin was so greasy all the time that it felt like I'd been wearing the same clothes for a week, just an hour after putting them on, but then my skin finally adjusted to the new normal.
My skin is soft - much too soft for a man of my age, according to my wife. I have no body odor, even after a heavy workout where I'm still covered in sweat. I can (and have) gone for week long hikes and come back not smelling bad. Contrast this to before where an hour after a shower I'd smell terrible if I didn't put on that nasty underarm deodorant (I don't use that stuff anymore, either).
My father was skeptical when I told him, but eventually I won him over and he experienced something similar when he stopped using soap to wash.
Soap is only for things you can't remove any other way (like motor oil), or for when you need antiseptic conditions.