So I was cruising on the low difficulties so I bumped it up to Prince. The game has REALLY started to shine for me.
I was never good at Civ IV because I would always get crushed militarily. Not so with Civ V.
In my game (playing as America), I was cruising along, acquiring land like nobody's business. I start noticing some Roman troops on my borders. I keep building up my cities, and then bam -- Rome decides to attack.
All of a sudden I'm screwed: I have no gold, my people are unhappy because I have too many cities and improvements, and my troops, while at least on the level of Rome's, are far fewer in number. My military advisor is telling me to do whatever it takes to get peace with Rome, because they have an army capable of conquering the world and the war "threatens our very existence."
Luckily we're not at the point where Rome has ships really, so looking at the land mass I see they have to go through a few cities to get to my main American ones (I had just taken advantage of a city-state's war with Songhai and wiped out Songhai only 15 turns beforehand, with very few necessary troops). Adding to my civ's unhappiness was having a bunch of new puppet states out on the perimeter. Luckily these were going to be the ones giving me a buffer.
I switched all my cities to making minutemen, and switched all of the cities to production focus. I went in an annexed one of the cities I had just taken over and razed it to the ground so I didn't have to deal with the unhappiness there. I start to pull all my troops over to the west to face Rome, with the intent of slowing their progress eastward for as long as possible, until I could get some Minutemen to back them up.
As luck would have it, I was keeping a Great Person for a rainy day, and I busted a Golden Age. I was making some good money again and the Minutemen were humming along.
And here's where the game came alive: the combat is SO much better! Using the bombard ability of my cities and a few archer units I was able to weaken the oncoming attackers and funnel them into melee units that could finish them off. Still, wave after wave finally fell. Rome was at the doorstep of Boston.
But then, my legions of minutemen were at hand! Six cities building minutemen nonstop led to a first wave that kept Boston safe, and then the second wave began to push them back. My military advisor said the war was going well, and to keep on the offensive! The tide had turned. I ended up pushing Rome all the way back to its original borders. With Caesar beaten up, it becomes an all out brawl as Arabia decides it wants a piece of the pie, and starts taking over northwestern Roman cities as I push in from the east. I race to grab the one Roman city I had my eye on and settled into an uneasy border truce with Arabia.
10 turns later, Japan shows up out of nowhere and settles in the middle of me and 5 other city-states. Shoot to the present time, when Japan and Arabia simultaenously declare war on me. I quickly take out a nearby city-state to get Belgrade on my side, who luckily is militaristic and starts giving me top-tier (for the time period) units and starts fighting off the just-landed Japanese in the east while I face Arabian troops in the west. The funnel strategy begins again, only now I'm fighting a war on two fronts.
MAN I LOVE THIS GAME