I don't know if these ideas have been presented before. If they have, consider this my support for what previous writers have said in favor of them. That said, let's start with...
City Radius: A city may make use of all tiles within its radius, not just a certain maximum number. With this caveat, only those tiles actually under a city's control. Which tiles are under a city's control depending on the city's culture. So if a city has a five tile radius, then that city would be able to exploit tiles 5 deep.
Conquest: A player may choose to occupy a captured city instead of annexing it. If occupied it is to be returned to its original owner upon agreeing to a peace treaty.
Peace Treaties: War ceases when an armistice is declared or imposed. Combatants may then engage in treaty talks, working out adjustments of borders, allocation of resources, and payment of reparations along with any thing else the participants can think of.
Technology: Once a discovery has been made, a technology invented, it tends to spread. Thus, for every civilization that knows a technology other civilizations can gain a bonus when researching that tech. Thus if the bonus is set at 5% of available science production, three civilizations knowing the secret of a particular tech would mean any other civilization researching that technology would gain a 15% bonus to the science production dedicated to the task of researching it. In short, the more people know of and about a bit of knowledge the easier it becomes for others to learn about it.
Retreats: An unit, fast or slow, being defeated in battle may choose to retreat. The chance of successful retreat depending on unit speed, comparative technology, and how damaged the victorious unit is.
Combined Arms: Two or more units may combine their strengths, with different types of units having a synergistic effect. So that musket and pike together, for instance, would have an advantage over enemy units they would not have alone.
Resources and Unit Costs: Units requiring certain resources would cost more the further from the resource they are. So a swordsman (iron) built in a city say 5 movement points from a source of iron could be built quicker than one built in a city 25 movement points away from that source.
Mines: Mines may not be built on grassland, flood plains, or prairie.
Irrigation: Renamed farms. Restricted to grassland and flood plains.
Ranches: Available only with the development of the right tech. What the right tech might be I haven't the foggiest idea. Restricted to prairie. Prior to the tech being developed a civilization may establish minor tribes on the prairie herding animals on its behalf. But such tribes will have a tendency to rebel and go marauding.
Civil War: During times of drought, war, and social upheaval civilizations will have a tendency to break up into factional fighting. Most likely in despotic regimes. Chance of a city joining the rebellion depends on happiness, distance from the capital, and the presence of certain factions antagonistic to the government.
Don't ask me for any ideas on how to implement these, for I haven't the slightest idea on how to do it. All this is is a list of things I think would be fun to include. Discuss amongst yourselves.