Children should be writing thank you notes for holiday and birthday presents. And, YES, they should write one to every person who attends a b-day party.
A thank you should be sent for gifts received, a nice gesture, or if a friend/colleague attends an event that you are running (fundraiser, a child's graduation, etc) or to a teacher who has gone the extra mile for your child, for a sports coach, etc....
You can never be too gracious!