I'd like to suggest a new type of record: the most vassals and the largest HRE membership.
72 imperial princes, in the order of icons:
Bosnia, Bulgaria, Greece, Serbia, Wallachia, Prussia, Corsica, Guyenne, Provence, Aachen, Anhalt, Augsburg, Bohemia, Brandenburg, Braunschweig
Austria, Hesse, Cologne, Sachsen-Lauenburg, Lothringia, Luneburg, Mainz, Munster, Palatinate, Pomerania, Salzburg, Switzerland, Thuringia, Trier, Ulm
Wurzburg, Wurtenberg, Navarra, Galicia, Ferrara, Genoa, Milan, Naples, Papal, Saoy, Siena, Tuscany, Netherlands, Crimea, Georgia
Golden Horde, Kazan, Pskov, Russia, Sibir, Polotsk, Yemen, Najd, Syria, Morocco, Ashanti, Ethiopia, Mali, Songhai
Swahili, Mutapa, Hausa, Kanem Bornu, Oyo, Mongol Khanate, Manchus, Oirat Horde, Baluchistan, Mewar, Sindh, Hausa.
13 non-imperial vassals: Sweden, Scotland, United States, Brittany, Castille, Granada, Ukraine, Tripoli, Tibet, Zhou, Gujarat, Nepal, Punjab.
Complete list in one screenshot. I haven't counted from this screen, but it should probably add up unless there's a bug of some kind.
Total sum: 84 vassals, as Ethiopia. Game began in 1.2.x and ended in 1.3.x.
I'd love to see my betters creating an even awesomer and cosmopolitan HRE.

The background is the coalition, other than a couple of revolt states (Haiti, Louisiana and Brazil) the rest of the world is either 'in' the Empire or 'in' the coalition.
Maybe I should challenge highest vassal income as well? That actually is my primary income in this game... IIRC.