I agree with everything TravellingHat said, but I already have my own list so I'll just dump it in here anyway
Most of my proposals are geared towards a more roleplay-happy empire building game rather than theboard game concept. Some people like that, and perhaps they should make an updated CivRev for those folk. The flagship of the series though, ought to be something grand. I really apologize for the enormous wall of text to follow, but it's a concept I've put some thought into and I'd like to just toss it all out there, don't read if you don't want to
I) Expanded Diplomacy/Foreign Affairs. Civ V diplomacy was a big step forward but also a step back. It's less of a numbers game from IV, and adds cool features like Denunciations, however it lacks some of the depth and capability of IV. Specifically, I miss concepts such as capitulation, peaceful vassals, and the way resource trading work. Trades shouldn't be arbitrarily limited to certain turns, they should just remain active until either party feels like canceling it. I have some specific proposals for how it should all work.
The first type of diplomatic interactions you can conduct (other than war), is friendship declaration andopen trade. Open trade permits basic commerce between civs (working pretty much as it does in IV), and allows for the diffusion of technologies(if one civ researches a tech that the other doesn't have, the lacking civ gets a boost in its research towards that technology). This would also permit non-combat units to move around in each others territory (incl. missionaries). It would also make spying easier between civs(there would be a percentage hit to counter-espionage). As a deterrent to opening your borders to just anyone however, the AI would exploit the opportunity to scout your territory and look for weaknesses in your defense and unit placement. So one would think twice before allowing right of passage(which is actually a better name for the idea...) with a much stronger Genghis Khan
. Open borders is the same thing, but enables cross-border stationing of military units and their travel.
We should also be able to conduct larger scale diplomacy, spanning more than just two civs. I've longed for the ability to engineer a grand military coalition between like-minded civs. Basically you can sign an alliance with one civ, and then invite a third tojoin a coalition, which would bring that civ into alliance with both of you. Seems interesting no? It might not work out though if game-breaking super empires just go around gobbling up the map. I like the idea of robust alliances though. You get the idea.
II) The return of the Civics. I'd like to see a robust system of civics covering all aspects of the empire, switchable at will(with the anarchy penalty of course). You can unlock and change between systems of government, power structures, military policy, all sorts of stuff. Go look at Rise of Mankind for a good example. Later civics are not necessarily better ones, they just give you more flexibility, each has it's own benefits and drawbacks. This makes running a civ much more immersive and interesting than simply a bunch of cities and armies. You can build a truly unique society.
Speaking of that, social policies don't necessarily need to die(it was an interesting use for culture after all). Remember the various leader traits from Civ IV? Perhaps those instead can be converted to social policy trees that you assemble, much like G&K religions. Ever play a civ with a seafaring trait and then spawned far inland? Kind of silly. You are the leader after all, a guy at the computer, build your own traits to distinguish your rule, adapt to the situation.
III) Culture and influence. The way culture worked in Civ IV was great, for the most part. Tile flipping was a good way to stop some upstart loser AI from plonking a city in the midst of your growing cities to nab a resource, cause it would just flip over. Also, if he has a city that's closer to yours than his, why wouldn't your culture naturally take over?
IV) Keep the city states, add the City State Diplomacy mod into the main game. Nuff said.
V) Armies, stacks, and 1UPT. The move to tactical combat was a marked improvement for the series, but the strict implementation in Civ V is just broken. Stacks of doom were replaced with carpets of doom and traffic jams. It was fun, but also could become incredibly annoying. The designers also had to cripple production to make it work, otherwise the resulting big armies would make the traffic jam situations even worse. To fix, I'd like to borrow a concept from endless space and adapt it to Civ. For those unfamiliar with that game, you can put your ships (armies, in this case) into fleets, but they were limited in size by command points. Small, weak units used up less command points than larger more powerful ones, and as you worked your way up the tech tree, you could expand your CP per fleet allotment. I think a similar system could work for civ. Basic infantry units use few command points, light cavalry would use more, heavy damage dealing knights would use more, siege weapons would take a LOT, and so on. This system would nicely prevent stacks of doom without killing off the tactical combat we have now, and would also prevent traffic jams. Players would be encouraged not to build stacks unless necessary; there would be flanking bonuses for occupying adjacent hexes to enemy units(much like now), but you can do cool combined arms stuff too. Perhaps a system of collateral damage could be implemented when attacking one of these armies, where spillover damage would be inflicted on the other units in the army, that weren't actually taking part in the combat. I'd invite some discussion to hash out the details on this.
Another interesting idea, units that get promoted high enough gain special commander abilities when put in an army, and provide bonuses to all the units in that army. This would be good encouragement to hang on to valuable units and keep them safe.
VI) Ecology. This falls firmly into theimmersion territory, and gives you something else to worry about. Different games(and not just in the civ series) have implemented this in different ways, with varying degrees of merit. Basically, pollution and environmental damage are a factor in the game. In the early game, the most damage you can do is chop down a bunch of trees, and you won't see any effect from this for a while. Just like in the real world, you need to develop that land to suit your needs, the consequences won't be felt until much later. Once the industrial era hits, depending on the buildings you put in cities, pollution can become a factor, eventually degrading the performance of tiles. You can try and clean it up, or just ignore it. At some point, you may start to slowly notice some changes. Grasslands start to turn towards plains, and desertification becomes a problem. Eventually, you have to research and apply advanced technology just to keep your tile yields up. The ice caps start to melt, and coastlines change. Cities built on the coast are at risk of being flooded and destroyed if they don't build the appropriate countermeasures. There are civics you can adopt to lessen your environmental impact, and you can pester the AI to adopt them(of course, they can do the same to you). If things start getting really bad, and more and more tiles get turned into deserts and swamps, it can even provoke wars as civs try to evacuate towards better land or punish highly polluting neighbors. But of course, you can fix the planet! There are a couple different ways to do that.
A resolution can be passed in the UN mandating the adoption of more responsible civics, that's one way.
The other is a massive world project, undertaken by any one civ, to completely and permanently solve the problem. I think Call to Power had something like this, I'm not sure. The civ that completes this project earns points towards the victory system...
VII) Mastery. If you've never played the popular Civ IV modRise of Mankind, you should do so. Not only is it a lot of fun, I pretty much stole this entire concept from there. Basically, all the individual victory conditions are eliminated, replaced by one, the mastery victory. All this does is calculate your performance in the various areas(domination, power, techs researched, launched a space ship, runs the UN, wonders built, cultural level, solved global warming, etc), adds it all up into a special score after all turns are done, and the civ with the highest wins. It forces you to play a balanced and adaptable game, but doesn't exclude the smaller civs from potentially winning as well by working hard to exceed in certain areas. You also don't get(IMHO unrealsitic) last minute rushes to arbitrary victory(I need to get this spaceship into the air before that other guy gets the UN up and running or it's all over!). Which brings me to...
VIII) United Nations. Every civ players favorite tool for world domination. Not too much different here, it's built, elections are held for a secretary general who tables resolutions, everyone votes, etc. The main difference is a lot more resolutions, and it's less binding than the fascist dictatorship it was in Civ IV. Participating in the UN process has diplomatic benefits, and defying it carries penalties. The UN can start wars to bring rogue civs into line, and end them too. It can reassign conquered cities, and mandate certain civics. It can also limit the use of nuclear weapons(but not ban completely, that would be no fun). It changes the flavor of the game from brute force and anarchy of nations into diplomatic guile and collective security. If wars are fought after the UN, they're usually big ones. To avoid pissing people off, the UN is optional when starting a game.
IX) Stability and revolution. One of the biggest forces of change in human history is rulers losing control over their empires. I think Civ VI should reflect this. Tightly couples and well connected empires are more stable than loosely connected ones with cities all over the place. Distant cities with few ties to the capital may start to flirt with the notion of independence. Unhappy cities may revolt in protest of incompetent leadership, and may ultimately result in civil war and independence if you don't deal with the issue. Certain civics, expanding and conquering like a madman, and significant minority populations in your empire can also cause unrest. You have to take care of your empire to ensure it remains yours, legitimacy isn't handed to you on a silver platter. As a rule of thumb, people don't like long protracted wars where scores of soldiers are sent into the slaughter(masterfully executed wars can give you some nice benefits, on the other hand), followers of religions other than the state mandated one(assuming you have such a thing) are also no good for business. It's pretty obvious stuff.
X) ICS. IMHO Civ IV nailed this. If your expansion outpaced your economy, you boned yourself. Large empires are advantageous, but you have to pace things and strike a balance. Needless to say global unhappiness dictating everything is the first thing out the door. A global happiness mechanic as an average of all city happiness weighed by population is a good modifier for some empire wide stuff, but it's not the holy grail it is in Civ V, where it exists solely to fulfill the Schaferite vision of tall empires. You shouldn't have to choose between wide and tall. If you play smart, you can have both.
I'll stop there I think. I've rambled long enough and I typed the entire thing on an iPad, which is a special form of torture