I quote myself:
Some simple, doable, enhancements to culture:
1)culture units, units that emit culture just like a building. Mission, televisor, publisher
2)culture instead of ethnicity; culture is in citizens, not in land
3)migrant units, cost pop, can merge with enemy cities to become citizens of their nation that retain your own culture
4)cultural spies; an espionage option of attempting to convert citizens to another culture
5)cultural hybridization: by doing something, say building a building or researching a tech, you can assimilate another culture to become a new culture that encompasses both. For example, as the chinese you could assimilate the mongol culture creating a sino/mongol culture, and instantly all citizens in all cities which were either chinese or mongol would have a chance to become sino/mongols (the culture you would now be playing for the victory of)
6)you would play a culture, and win when it won, either politically by the usual methods, or culturally by encompassing a percentage of the worlds citizens. you would control the political destiny of all cities dominated by your culture, unless they were dominated by someone's military.
7)new cultures would also spontaneously arise, and sometimes hybridize
8)culture flips would be capable of creating new political entities
I guess I should add:
9) emigration: if a citizen of a city is of your culture you can make that citizen into a migrant unit, even if you don't control the city.