Here in civilizationostan, we don't have such silly greeting rituals.
We say hi. And shake hands if it's a first time meeting.
Why go beyond a handshake and a hello unless you're planning to depants the other person?

Uh... Huh? Where did 'whatever comes naturally' go?
you win the thread.
edit: Oh, yeah, left... Damn it, I'm a sheep!

Men, left or right, doesn't matter.
Women, middle.

East. ALWAYS east.

I've only ever really hugged 2 people and they're both way shorter than me so instead of left or right I go over the top.
My expectation was to see everyone going right since right handed is most common, perhaps its the inverse for hugging

This.
And I don't have an excuse for it. (I mean the philosophy thing, btw)

It's kinda hard to tell as there's always two boisterous little girls who try to squeeze into the middle. However, when holding either of said girls, I hold them towards the right (so I guess that's my head on the left), so that it's easier to see the stairs/where I'm going.

Normally, left.
However maybe the bigger question might be how do you place your hands? Left hand under the other person's right hand, your right over their shoulder, or vice versa, or both hands around the neck?

hands one-above-the-other on the small of the back for girls. which is really what's important here.

Go left so you can shake hands at the same time if required in a manly handshaking hug kind of way.

Usually I go over their head. Yes, and then wrap my hands around them and come around my own back.
Yes.
Actually, its left. Then my hands go under their arms, in their upper back and try to reach my elbows. :)

Another vote for the left side.

Left.

middle as i am taller than most girls and their head ends up on my chest.

I have a reputation at work as a guy who hates hugs.I don't actually hate hugs, I think the occasional hug is awesome. I just think excessive hugging ( like friends who hug each other every day) is kinda stupid.
I hope I didn't offend anybody with my super controversial last sentence