I am new to the discussion, so I will be adding my "vision", while gradually going through the thread. I may repeat some things, but perhaps people can take what I write, expand on it, or incorporate it into their own views.
My overall motivation in my design for civ 5 is the following. It is still to be a strategy game, not a reality simulator. 'However', many of the most influential factors in the history of civilization should be incorporated, in a way that is relatively true to how they behaved in actuality.
For example, culture is very dynamic, as we all know. Yet in civ 4 it is just a matter of land control.
Resources, and the abundance with which they are owned, has been a dominant force in history. Civ 4 makes resources relatively important, but trade does not explode when, for example, a civilization has 8 tiles of spice, and other civilizations have none. A civilization with an abundance of oil cannot make more tanks and planes than a smaller civilization, which would run out of oil and need to rely more on manpower.
And so on...both game play and entertainment value are important, but so is keeping to the spirit of true history. And in doing so, I believe the game would have a natural cohesiveness and playability that would be hard to match. Not to mention the players' intuitions would then serve them very well, since they have an awareness of the real world and how things work.
Here are some preliminary ideas. I will likely add more in future edits, especially if people are interests. For now I will avoid combat, as there is much to it, but good combat would depend on the rest of the gameplay, and has to accommodate the non-combat game.
CULTURE: Culture needs to be more dynamic and more faceted. A nation's culture effects how productive it is, how willing it is to expand, so on. For example, Manifest Destiny was a cultural phenomenon which greatly assisted in the expansion of the American empire... as did many other religious movements which motivated people to spread.
An easy way to envision the "cultural system" would be like the current civic system. There would be different attitudes that could be adopted by a nation. For example, "views of the afterlife". Ascension to another plane, wandering the earth as spirits, reincarnation, so on, all could have practical effects on a civilization. With spirits, people are more likely to stay in their homelands, as to not leave their relatives behind. With ascension to a another plane, the development of Gods and modern religions could be hurried, leading to more "advanced" or organized religious societies. You could see some civilizations go far into the modern age with keeping their views of spirits and reincarnation, while other civilizations "advanced". Reincarnation could make people more respectful of nature, resulting in lesser ability to exploit it for resources, but more happiness and richness of life (culture points or some such).
Only the more major cultural values throughout history would likely be included in the cultural system, as to not make it too complex, but still make it rich. Much of it would also be automated (although determined often by how the player acts) so much of it could just be ignored at times. But it would always effect things. Sometimes it could make a forward swing and help the goals of the human player. Sometimes there could be a cultural backlash and a changing of values, which impedes the player from his current decisions. Throughout history culture and values have ebbed and flowed, it would be no different here. Unless you truly made it your aim to make it static (low education, closed society, police state, so on).
At the very least, sharing views on the afterlife, etc., would make a civilization more friendly to other people who share their views.
There could also be "degrees" of attitudes. A simple example, would be "tolerance of outsiders". This would go from very low to very high.
With high tolerance, trade and sharing of ideas is higher, leading to more research, more money, but also, more impact on the nation's culture. You, the player, would have less control on your nation's values, if you led a high tolerance nation.
With very low tolerance, a nation would have low levels of trade and cultural influence, yet this would make the civilization able to be more stable and controlled, as it's "cultural system" would not be altered.
War effects tolerance greatly. The impressions other cultures make effects tolerance (a nation which has only met other nations it dislikes will be less tolerant). Education and the advancement of ideas effects tolerance... so on.
Some cultural aspects would make relatively minor effects on the game. Some could be very major, and determine a turning point in history. For example, the "nationalism" tech in Civ 4 is a cultural movement. "crusades" could be another development, which is a cultural movement.
You could choose historic civs with pre-determined starting cultural values. You could also create your own custom civ with cultural values, although some combinations would not be possible because you'd have to "purchase" the advances to make those values available at the beginning, or allocate points to set a slider for a certain value at very high or very low, increasingly so as you get to the extreme ends.
RESOURCES:
It is paramount that abundance of resources matters, instead of just "having" or "not having". A civilization with 3 coppers could leverage it to become a dominating force in the ancient period, even over those with 1 copper. Of course there would be things to balance this out, but the 3 coppers would be a matter of great importance.
Copper = weapons. Now, having more copper doesn't mean you necessarily make "better" weapons, but you can make more. So what would seem a natural possibility, is, the more copper you have, the faster you can build units.
However, an army isn't just a bunch of copper. You need soldiers, too. So there would some way to incorporate a "human" and "equipment" component to each unit, perhaps each consisting of 50% of the cost, although this would vary with units (the limiting factor for riflemen was usually manpower, so that may be a 70-30 cost).
So the player with 5 coppers would get, say, a 50% production bonus to metal equipment, making them able to quickly produce heavily armored infantry(heavy infantry would require more copper, as opposed to manpower), or quickly produce the equipment requirement for lighter infantry. While, perhaps, being light on the manpower aspect for the infantry. This could make interesting alliances where one nation with abundant hills and copper supplies a large farming nation with copper for weapons.
The ability to produce and maintain the "human" component would depend on many things. How many people the nation has in total, it's cultural values and willingness to fight or be conscripted, how much money you are willing to pay units (if you pay more, more people will be willing to enter your manpower pool).
PRODUCTION:
The system of production, where for normal production only a city can contribute to the projects inside it, should be altered. Workers and resources from all over the empire could be brought to the capital, to produce an immense wonder, for example.
However, it would all come with penalties, as opposed to only relying on local production capability. You would have to pay more money for labor, you would lose some overall production, you would use some more resources. When a player decides to re-route resources they will be notified of estimations for the penalties (could be a small random range). "collection" and distribution of resources (metal, wood, etc.) should not have to be controlled by the player to play well. The system should be user-friendly, yet still realistic. A player could go much of the game with never looking at the national pools, although they will not do as well.
However, there does need to be a variety of resources instead of just "hammers". Wood, stone, metal, so on. Later on in the game some would just be taken out of the pool as they become insignificant. You don't have to keep track of your stone once you reach the industrial and modern age.
So, all the resources could be collected and put into national pools, which are displayed to the player (100 wood production, for example, 1000 wood in your pool). If you run out of wood supply your production will not "stop", but you will just build more slowly. Just like with the copper for units, it just increases production rate. Wood would, however, naturally accumulate, as you don't have to "tell" your nation to go and collect wood, it just does.
So each city will tend to have wood available. However, you could put special emphasis on it, for example, shifting 70% of a cities laborers to lumber gathering, leaving 30% for stone collecting. If anyone has played sim ant, it could be like the system in that game, where you set your percent of ants to "nursing, gathering, building", simply by sliding a pointer on a circle display... if you slide it all the way to nursing, 100% of the ants would nurse.
But enough with possible details, as those could easily change... it would just be a highly automated resource system, that you could adjust to build up stores of resources, although there could be a limit to how much you could control it, and manipulating it too often or too greatly could bring about waste. As is the problem with a controlled economy, versus a natural one. (another idea for cultural values, libertarianism versus collectivism, could effect the dynamic of this, and other things).
RESEARCH:
Research should NOT be as directed and controlled as it is. Breakthroughs often come through personal efforts of random individuals, depending on the nation's surroundings and interesting. So, if this were applied in Civ 4, if you had 4 cows nearby your civilization wouldn't randomly research fishing. The people would quickly get around to researching the cows, and how to utilize them.
However, the government can also direct resources towards specific discoveries. But they would not be able to mobilize the whole nation's scientific potential for this.
So there would be multiple forces effecting research. Interaction with foreigners would also play a significant role, going back to the "intolerant" versus "tolerant", although only certain techs would be exchanged this way, for example many military technologies would not (nor would those military technologies typically be researched by the people, but only the government).
Also, there should be a degree of randomness in the tech tree. You CANNOT depend on opening up the path to a certain technology. In Civ 4 the tech tree is dynamic in that there are multiple routes to different technologies, but you always know any of those paths will unlock certain technologies.
Pre-requisites would increase the odds of "eureka moments", which would then unlock techs so you could put direct effort into a technology, to advance in a certain direction. But you will have to play to the development of science, you will not determine it yourself. You would not be able to know what technologies you will specifically get, or be able to get. But you can promote scientific endeavor in your nation, so a citizen is more likely to create the first working plane, or invent the light bulb.
There could be games where the telephone comes before flight, and vice-versa, and you could not know when these moments would come, although you can encourage them.
A small island nation could have a breakthrough in flight a significant amount years before all the larger ones, possibly bringing previously unheard of prosperity and foreign interest, or perhaps encouraging espionage.
However, military research would often be more predictable and directed. So players would not really get into situations where they lucked out in regards to a military technology, and were left in the dust. However, an isolated nation may go half a century longer without gunpowder, and have to rely on military prowess in other areas (which they could direct research in, for example, they don't have gunpowder but become very, very refined in archery, horsemanship, or infantry logistics, and can stand up to gunpowder armies).
One thing to note, is what has naturally emerged from my "rules"(ways to implement reality), is that isolated nations can develop very specialized and distinct cultures. They are more likely to master a type of military, out of necessity. They are more likely to develop a culture, which they stick to, and develop strong conviction in. This would also work for groups of nations, which would influence each other's cultures, but not be influenced by ideas of distant nations. You could have large "clashes" of ideas, as worlds meet, perhaps creating geographic wars, or distrust.
Even in multiplayer players could be driven to war in this way. The will of the people, of the culture, would be to go to war against those with very different, or even offensive ideas. The player could 'possibly' receive backlash if they didn't go to war (in a very aggressive society), or they would at least be passing up the opportunity for a relatively 'smooth' war, where the people were very gun-ho about fighting.
POWER
Windmills, watermills, power plants, and so on, should all be part of a national power system. A humongous city may require power siphoned from large tracts of the country (like, power from the area of 3 cities, in civ 4, could be directed to one city). However, the more distance the power is transported, the more waste there is, and the more expensive infrastructure is. So there would be algorithms somewhat similar to distance maintenance, in Civ 4. However, the maintenance would be paid in wasted power also, so if a nation had very short supplies of coal, natural gas, etc., they would have to take care to localize power, and perhaps not be able to sustain extremely large cities, or just have very polluted cities full of coal plants. An industrial era should 'definitely' be in there, during which most power would have to be localized, first in the form water mills and such, later in factories. Later technology would bring ability to transfer the electricity through large power grids.
EXPANSION
Expansion of population should have some automated elements to it. Cities should spring up in desirable places, or wither away if the area is no longer desirable(most of the citizens would return to other cities). A city with many attractions should automatically have people flock towards it. A large city without attractions will likely stagnate, or have people leave to other cities. This would actually make culture partially necessary to have a production or science monster of a city. It will be hard to have a huge workforce if people don't like living there (not that there aren't ways around that, slavery, etc

).
The player would be able to play a large role in expanding, directing people to settle in certain areas, and tell them what to build there(farms, mines, etc.). However, this would have more of a cost than natural expansion(it gets progressively harder to tell a nation of people to move around at your whim), so the best strategy would rely on both to certain extents, perhaps deciding which areas require more directed and aggressive settling (border pushing), while allowing natural expansion in other areas.