When you hug someone, which way do you try to go first with your head--left or right? I want to avoid as much awkwardness as possible by going with the statistically likely one. Otherwise you end up doing the little sideways head bob thing for a few seconds and the flow is just totally broken.
I tend to go left at first.

Left, but it also depends on the position of the other person.

Yeah, the position of the other person is a big factor. Not often will hugging commence when you're both standing bolt upright and directly facing one another.

The cheek kisses is an easy one to deal with, just don't go for a tight hug and that way the other person has room for the cheek kiss while in-hug, thereby not making either person feel awkward. Plus if the other person does go for the cheek kiss, its an easy recovery to do the same. You don't really have to actually make cheek/lip contact for it to work, just making kiss sound near the face is enough

Left, I think, but it's not a conscious decision.

Tee hee. You have a burning poll/pole :p

Left

hope they can't feel it when i go in for the hug

Left

Left

Left, but boy do you think things a lot.
Just do it as it comes natural. Unless you are hugging Stalin, you will be ok.

Right
Left
ABOOOOUT TURN

I don't hug.
I am lonely.

I hear you can get an ointment for that.
More on topic, I also agree with LEFT.
To summarise, left is right. right?