I played Inca on a huge world at marathon speed.
Inca set forth several Quechuas at the inception of its settlement, and fattened them up on animals and Barbs, always choosing the "attack city" upgrade. The early years were all-out war against all and anything that came into the range of ancient, and still quite savage, Inca.
One by one, Inca located the other civs on its continent, attacking each civ methodically, the closest first. There were 4 other civs and each capitol was located on flatland, none on hills. Amazingly, each capitol was poorly defended so each one fell before the armies of Inca, one after the other. Germany, France, Japan, England -- cultures all destroyed, but their cities were saved, to serve the glory of Inca.
Of course, Inca economy and science was stifled with the added cities, but that was solved by Inca adding city buildings via slavery. Inca grew and prospered under the barbaric whip.
As each former capitol became assimilated into the "Way of Cuzco," Inca then allowed the Barbs to build cities, thus saving settler production in Inca lands. As the Barbs created a city, Inca strategy was to take out one defender while leaving the second defender, until the Barb city reached population 2. Then Inca took over the Barb city, adding it to the Inca Empire.
As Inca economy and technology recovered with markets, libraries, banks, and wonders too grand to enumerate here, Inca took the lead in techs. As soon as pirate ships became available, Inca built several and sent them across the seas to terrorize hitherto unknown Inca enemies for a few centuries, implementing the iron discipline of Inca, "Ocean-Admiral and Ruler of the Seas Supreme."
The pirate ships generated quite a few great generals who Inca saved to build the military academy in cities just on the verge of having good military production (lifting those cities into good military production). Thus was Inca power multiplied and feared throughout the world.
After establishing unparalleled military might, Inca then shifted tactics into culture, and is very close to a cultural victory. Inca is now the shining civilization across the water, the jewel of the world, defender of the meek and innocent, benevolent master of all -- a true iron fist in a velvet glove. Don't mess with Inca.
Alas, Civ5 comes out tomorrow and I guess Inca won't be able to realize its destiny.