Depends on your definitions. Great Britain has a "constitution" which is not a single, written document. The Magna Carta is part of it, and dated from 1215.
Also: Poland, France, Germany, Spain, Portugal, pretty much every European nation.
Edit: Seems that GP conflates "nation" and "state". If we're counting continuity of government, they probably only Great Britain is a good example, other countries had undergone many changes, from absolutism, to constitutional monarchy, to non-existence, to democracy, to fascist dictatorships.
There's quite a bit of change in Britain as well. There was a fascist dictatorship from 1649 until 1660. Nor is 1688 insignificant. (And it's only Great Britain from 1707).
I'd argue that France has changed a lot more during the same time, at least regarding the regime changes (from 1788: monarchy, constitutional monarchy, republic (1st), dictatorship, empire (with Napoleon), monarchy, republic (2nd), empire (2nd Empire with Napoleon III), republic (3rd), fascist dictatorship (Vichy), republic (4th & 5th)).
There has indeed been a lot of change - the UK in its current form only dates from 1922!
However, the lineage of the what is now the UK does stretch back in places over a thousand years to the creation of Scotland and England as separate unified kingdoms in the 9th & 10th centuries.