Play as the Vikings on Marathon and try to get to America as soon as possible (as per UHV, so by settling Iceland). But once you've settled Vinland, don't stop but send more and more settlers so that by the time the Europeans arrive, they find the entire continent colonised already.
Playing as Rome and recreating the full Roman empire in the classical era, then taking it all back after the Europeans spawn (or doing the second as Byzantium) is a favourite of mine.
Playing as Carthage, worldbuilder the Suez canal in and set sail for Australia to play as the Australians. Look out for the Romans beaming their troops in, though.
Play as the Mayas and go all reverse-conquistadores on Spain (or any other Europeans you like).
It's not exactly a build, but quite fun nonetheless. Play as Babylon and WB your units away, putting a single scout on Antarctica instead. Next put an independent Babylon into place. Exit worldbuilder, press Ctrl+Z (with chipotle, of course), and watch world history unfold.
One that I had fun with a while ago is Hungary. You play as England and instantly send your Settlers to found Budapest (at the bend in the Donau) as a capital, leaving England empty. It's the most cramped game you've ever seen with Germany and Byzantium breathing down your neck, but can be quite fun.
