Okay, I believe I've pitched this idea before, but hopefully this time I'll be able to fully express why it's something Civ 5 should incorporate. The one thing that Civ needs is to play not in turns, but in years. 6050 of them.
No, I don't mean like a mega-ultra-Marathon speed. See, while there are 6050 years in a full game of Civilization, only about 10% of those will actually be played. So what's the point of it, you ask? Why to create a game with a more realistic and engaging flow of time, of course!
Here's how it works: You give all of your commands to units and cities, which will then be carried out as soon as you hit the End Turn button. (So this means all your units will carry out orders simultaneously when End Turn is pressed.) Once you end your turn, the years will pass and you will watch as your units carry out your orders. Eventually, the game stops auto-playing, and your next turn begins.
So you're saying it's just like the turn-based system Civ already uses, but between turns you watch your civilization carry out your orders? That doesn't sound necessary at all. Don't judge just yet, hypothetical critic of my imagination!

The whole point of this system is that it's much more fluid than playing in turns. Normally, the game will autorun for a predetermined number of years before starting your next turn. For example, in the early game, on Normal speed, after ending your turn, the game plays out 40 years and gives you your next turn. However, it will often be the case that your next turn comes early... say in 34 years instead of 40.
The reason your turn may come early is because an event occurs which requires your immediate attention. Events that warrant an early turn start include:
- Your unit has finished moving.
- Your unit has encountered a hostile unit.
- A hostile unit has been spotten near your territory.
- Your city has finished producing whatever it was making.
- You have researched a new technology.
- Your city is about to grow.
- A rival leader has changed the availability of diplomatic options (Open Borders, Tech Trading, etc.)
- A random event has occured.
An interface not unlike BUG will keep track of any events which require your attention, and when one pops up, autoplay will stop, and your turn will begin. So you may have your beginning turn, your next turn 40 years later, your next 40 years later, your next 3 years later, 39 years, 26 years, 40 years, 40 years, 40 years, 40 years, 24 years, 40 years, 12 years, 40 years, etc. The odd frequency of turns comes from important events.
Not only this, but the pacing of the game will change considerably when you are at war. Because each turn counts, turns will start coming once a year. This means wars can take just as many turns to resolve, but will occupy less of history. A 40-turn war will last 40 years, not 200. Once the war ends, the years begin to fly by again.
Some have also complained that the endgame is uneventful and boring. This system will resolve that issue: the years will not creep by when it is unnecessary. If your units are all fortified, relations with neighbors are peaceful, and your workers are all building railroads automatically, the game will give you your turn every 10 or 20 years by default, allowing you to plow through the uneventfulness. Meanwhile, the game will pick up on anything that needs attention (new orders, etc.), so the years will fly by only as long as there is really nothing to be done.
Basically, turns only come whenever there is something to do, and if there is nothing to do, then every few decades or so, as a precaution. The amount of turns which involve only pressing the red button are severely reduced.