Great Squares of the World

I have visited some of the great squares of the world - Red Square in Moscow and Trafalgar Square in London - but I've never been to Tiananmen Square. It's definitely on my list of want-to-sees. The picture is my mind's eye is very specific, but neither Red Square (much bigger) and Trafalgar Square (smaller) didn't match what I expected. There must be other great squares of the world, but none comes to mind at the moment. If I can generate a list, I might make it a check list.

We tried this once with the great prisons of the world. It's not a long list, but start with Alcatraz, Tower of London, Lubyanka (I didn't really visit Lubyanka but I did drive by it), and the Bastille. Okay, the Bastille doesn't still exist but there is a sign on a street corner in Paris marking the spot.

Additions:

1. Adding squares without searching the Internet as they come to mind: Union Square (San Francisco), Pershing Square (Los Angeles).
2. Duh! How could I forget Times Square?