If a child requests a hug, either verbally or physically, why would we not give the child a great, quick hug and send them off to work?  Would we not do that in other social situations?  We are modeling how to be human, and some humans are very physical in showing appreciation, love, etc.  So, of course we give a hug when requested.

What we have to be careful about is not to give hugs to satisfy our own needs.  If we need a hug, we need to get those needs satisfied outside of our work with children.  If we are asked for a hug, by all means, give one.  There was a time when teachers, parents, administrators were hyper-vigilant about physical interactions with children, but I think that period of our human history in education has passed.  So, if a child requests a hug, give one!