The hair we're left with (since we evolved from our ape-like ancestors) :
On our heads - actually to keep our heads cool - by preventing direct exposure of the skull to sunlight. Ask any bald man how much more sweaty their head feels on a sunny day compared with when they used to have hair.
Eyebrows - a natural barrier / channel to stop sweat getting into our eyes. Again - ask anyone who has lost their eyebrows how much of a problem this is.
Eyelashes - actually some of the most important hair on our bodies in terms of offering physical protection against things getting in or even near our eyes. Our eyelashes are connected to the some of the densest touch and movement sensors anywhere in the skin.
Nasal hair
I've got to say Lying Witch talking about getting her nostrils waxed has been the stupidest thing I have read on her. We are born with tiny hairs in our nostrils to reduce the risk of particulate matter entering the lungs. Pulling out the hairs from your nostrils significantly increases the risk of very nasty nasal bacteria getting stuck underneath your skin. So you saw a sign in a salon offering it...it wasn't an order!!!
Armpit hair
Primarily there to wick away the sweat that would otherwise sit on the surface skin. We would actually stay cooler if we kept it and then we wouldn't need to apply the carcinogenic chemicals on top...
Pubichair
Primarily there to wick away sweat that would otherwise sit on the surface skin. May also have an evolutionary role in diffusing pheromones.
Air on legs / arms
Mainly for the regulation of body temperature and to wick away sweat (as mentioned). Men have more hair because they also tend to sweat more.
It's natural. Anyone convincing you that it is better for you to remove it is trying to sell you something. When you do remove it, they can sell you even more stuff your body wouldn't have needed in the first place...stuff to treat the ingrowing hairs, antibiotics to treat the infected nostrils, breast cancer treatments..the list is long.