The little girl who curtsied to the Duchess of Cambridge was adorable, and I was impressed by her curtsey.
I have a question – does one have to curtsey to the President of the United States? Say for example if Barack Obama was visiting a royal and was undertaking a royal engagement with the royals, would a member of the public be expected to curtsey to either him or Michele just like they would to the royals? I'm asking because he is a head of state too, though I haven't really seen any photos of members of the public curtseying to him or past Presidents. (From what I've seen, the President and First Lady don't usually undertake engagements with the royals during state or introductory visits, but I was just giving an example of a situation.)
Nor would I be pleased, as a US citizen, to see that happen. No curtsying, please! 
I would say absolutely not!
One would never curtsey to an elected American leader, never. And technically neither the US president or his wife is supposed to bow or curtsey to royalty. But Nancy Reagan defied protocol and did it anyway and so has President Obama.
Jacqueline Kennedy curtsied to the duke of Edinburgh when he visited her in the WH after JFK's funeral. When chief of protocol Angier Biddle Duke insisted that the wife of an American head of state does not curtsey to royalty she replied "Well, I am no longer the wife of an American head of state".
I found it interesting that Presidents aren't supposed to curtsey to royalty. Why is that?
Ah OK, thanks for the answers; I'm not American myself so am unaware of the protocols.
I could see a slight bow of the head as a courtesy, and in fact I think we all do that to some extent when we shake someone's hand on first greeting. It's almost a reflex. But to bow in the sense of paying homage or respect/deference to the royal, no, for the reasons Moonmaiden indicated.
Thank you. But as with all history, it's up for debate. At the university level, in a Political Science course, I did one of my reports on Alexander Hamilton (and fell in love with the guy! ). I'm hardly an authority. There was a remarkable confluence of men at that juncture: John Adams, Benjamin Franklin, James Madison, Alexander Hamilton - I have my favorites. I'm not a fan of Thomas Jefferson, nor an un-fan - just neutral about him. Madison and Hamilton were more important imo. But this is wayyyy OT.
I think it is quite common for people to both nod and shake hands when introduced to someone.
There seems to be a special aura around HM QEII and the DoE. The queen is almost universally respected and admired for very good reason. Even Angelina Jolie gave her a little dip!
There are about three or four Royals that I'd probably pay that type of courtesy to, and QEII is one of them.
I agree that it was a faux-pas on the part of Mrs. Obama, but the gesture was a warm and spontaneous one in response to QEII, who had put her arm around Mrs. Obama first. Americans are not accustomed to the idea that someone can touch them, but they shouldn't touch back.
Michelle was in her early days as First Lady and it was obviously simply a lack of awareness of Royal protocol...no big deal, imo.
