And long may she reign !
Picture from the National Archives.
UPDATE - I hate to repeat myself but ...
The monarchy is the living totem of our tribe.
In the US, to be republican is to be an American patriot, in Ireland to be an Irish patriot, in France to be a French patriot. There is no patriotic British republican tradition - what republicanism exists is, often explicitly, anti-British.
Monarchy, like religion, appeals to the irrational in human nature.
I use irrational here to mean something which human reason is ill-equipped to grasp or comprehend, but which may nonetheless play an important role in human affairs. Complex or imaginary numbers could be an analogy. I can't grasp the concept of the square root of -1, yet it plays an important role in physics. (Note - there are also numbers known as irrational numbers).
A society can get rid of monarchy, just as it can get rid of religion. But irrational urges in human beings cannot be so easily removed. If they cannot be expressed via the structures built up in Britain over the centuries, they will find an outlet elsewhere.