I'm Byzantium. Doesn't seem so incredibly impressive for the time, but mostly because I pursued a much more informal empire policy. My proudest accomplishment in this game was
completely breaking and dismantling a France that covered most of Germany and half of the Iberian peninsula. I forced them to release country after country, and then liberally distributed GoI's and took advantage of the inevitable wars to vassalize most of continental Europe. Now Paris is in the hands of the Brabantines and France's capital is in South America.
I had Russia in mind for next (and this time they deserve it -- bastards are only ALIVE now because I helped them all the time early on in the game...then they backstabbed me later on to try and get my Baltic provinces), but after my first war with them, after which I forced them to release Novgorod and Lithuania, Sweden went and inherited Novgorod within two years. Sort of killed any motivation I had for taking on the Russian juggernaut.
Instead, I've got plans in mind to use that little shimmer of blue in the middle of Great Britain's American Empire (the USA) to kick Britain out of the new work and force them to release Scotland and Northumbria (and give Ulster to the Irish). After that, I'm not sure what to do. I'll have a few decades left, probably, but there's nobody worth fighting. Persia is pretty beastly on paper, they used to extend even further into China, but I invaded and took Persia Proper almost without trying and forced them to release Qin, Wu, and one other Chinese state, so that's a problem that will take care of itself as the Chinese consolidate and push out the Aryan invader.
I think I might just finally get around to retaking North Africa. I already dominate the parts that matter through alliances, vassals, or trade monopolies, but this is more for 'neat borders' than anything practical. I have three times the income of my nearest competitor (Castille) and the largest army in the world (now unchallenged since I decimated Russia). I've pretty much already won. I'm really most proud of my Baltic Empire and my American Empire; the Baltic because it was probably one of the most intelligent strategic decisions I've ever made in EU3 (specifically, taking Riga, Kurland, and Osel when me and Russia were originally dismantling Lithuania), it allowed me to easily project power anywhere in Europe without having to worry about ferrying troops from the Mediterranean. The Americas were a very near thing, pretty much a race north between me and Great Britain; me trying to cut GB off from Louisiana and GB trying to get past me. Ultimately, they took most of the Mississippi River but I hold the delta and a lot of the western tributaries.
What a fun game. Much more fun than I've had with the sort of games where you just go annexing each and every little thing you run across. My Empire proper is 100% Orthodox Christian, 60% Greek/15% Lombard (my other accepted culture), all cores except the far north of America and the southern Levant, and the richest, most developed on the planet. I've been very liberal with subsidies to my 'allies' in France and Germany so they're also rich and well developed. I've been HRE (via vassalage of 4/5 of the electors) for the three quarters of a century, having taken the title from France and then GB by cosying up to Corsica and vassalizing Trent, Genoa, the Salzburgian Papal States, and Messian.