Visiting the Plaza Mayor isn’t a bit like it was in the past (except for the pickpockets). You’re mostly going to bump into other bedraggled tourists.
You’ll get a much better feel for the history at the Museo del Prado, which has a painting of an Auto-da-fé in the Plaza Mayor of Madrid. Here you’ll see the unfortunate Charles II presiding over the Spanish Inquisition’s idea of entertainment.
In an auto-da-fé (“act of faith”), condemned heretics and apostates were brought before the crowds. There was a public procession and, eventually, an administering of the prisoners’ sentences. Some were acquitted; others were whipped, tortured, or burned.
If this is too bleak, the Museo de Historia de Madrid has lots of more lighthearted perspectives of the Plaza Mayor. All we’re missing today are bullfights, knights on horseback, and one or two nuns.