Most of the vitamins in kiwis are concentrated near the skin, and it contains lots of healthy fibre, so yeah I eat it whole.
Before eating it I wash it and scrub the outside with the scrubby side of a dish sponge, it gets most of the hairs off. I do this because after years of eating it hair-and-all, I finally managed to get one of the hairs lodged inside the gum of my backmost molar like a splinter. Hurt for weeks. So now they get a good depilation before consumption.
But yum! Skin!
To the people afraid of trying it: the skin is barely noticeable. It's the flavor/texture equivalent of adding a spoonful of water to soup.