Not that unique actually. Many (perhaps most) countries in Europe have some period in the past when they were much more powerful than they are now.

There's a reason why a huge portion of the population in the western hemisphere speaks Spanish.

And why quite a bit of Africa speaks French...

Perhaps not truly unique, but two things about the British Empire perhaps make it sting a little more:

1) It ended more recently than other European empires.

2) "The sun never sets on the British Empire". It was huge.

2 was also true of Spain at some point.

Plenty of countries in Asia too.

Russia happens to be in both, and it definitely suffers from this nostalgia.

Seems to me if anywhere Mogolia would probably suffer the most from this.

http://en.wikipedia.org/wiki/File:Mongol_Empire_map.gif

http://en.wikipedia.org/wiki/Mongol_Empire

Except it ended 700 years ago, not less than 100.

Unique? Portions of Italy have seen power come and go multiple times, if you count the Roman Empire. The Republic of Venice was still a going concern when the United States was in its infancy, and had been so for hundreds of years.