No one, including British subjects, are obligated by law to curtsy or bow to the queen. However, British subjects who want to keep with tradition and/or show respect to the royals may either curtsy or bow to them. A good rule of thumb is to keep it short and sweet, with a small, not-too-deep curtsy from women and a short bow (from the head only) from gentlemen. If you are a member of one of the Commonwealth realms (ex: Australia, Canada, Jamaica, etc.) you can also greet the queen with a curtsy or a bow. However, Americans should not feel obligated to curtsy or bow as they are not subjects of the queen. There are some Americans who feel the need to show respect to the queen with slight curtsy for women and a small, head-only bow for men, but it is completely unnecessary in terms of protocol. Trust us, no member of the royal family will be expecting any American to do anything other than shake their hand.