It's a tie between my first ever game of Civ ever about a decade or so ago (Civ 2, with teh Russians, Time Victory because I had literally no idea what I was doing. 10 years later, I still can't play Civ 2) or my first Monarch win in CIV. Screw that, it IS my first Monarch win in CIV.
It was a pretty awesome game. Continents, Huge, Epic, old Mansa Musa. I started on the west coast of a pretty round-shaped continent with, dig this, Montezuma to the north, Isabella to the north-east (both semi-blocked off by a really big jungle), Kublai Khan to the east and Huayna Capac taking the south. A religious warmongering freak, another religious warmongering freak, a backstabber and a psychopath.
It was a very tough act, juggling between each of them. There was an attempt at an early rush from the Incas, but it was short-lived and ended with a nice gold ransom, otherwise up until the 8th century all was quiet. Both Capac and Monty to the north converted to my precious Confucianism, which angered Isabella quite a lot. The resulting war saw a lot of fighting between them without a clear winner, and even though Monty dragged me into it (foolishly I thought that by pretending to help him he won't attack me later on) I didn't really partake in it in any meaningful way. Kublai Khan, the other Budhist on the continent, didn't help Isabella at all for some odd reason.
But then Monty came for me as well in the early 700s, ignoring both my help (sort of) in his war against Spain as well as our mutual religion. It wasn't easy stopping his long, endless and unrelenting waves of macemen and horse archers, but in the end I managed to beat him back and eventually we settled for an uneasy white truce. Tasting blood for the first time and having already gotten the war-machine rolling, I was ready for him when he DOW-ed me again at the beginning of the 15th century, and quickly managed to capture 3 of his cities and wipe two others off the face of the map. It was at this point that a very angry Isabella came crashing down on top of Monty as well, and seeing his cities razed to the ground made him rethink his position on peace and stability. I waved his offers away until Kublai Khan DOW-ed me out of nowhere, that Buddhist son of a... donkey. An immediate peace with the leftovers of the Aztec Empire, Isabella still pressing on mercilessly, I quickly turned my attention to Mongolia, taking one city, negotiating peace to regroup, and then immediately declaring another war. Hopelessly out-teched, the Khan stood no chance, and could only watch idly by as I took all of his cities and left him with one pathetic isolated tundra ball. Would have had that one too, if not for Capac, who chose to back stab me while I was up north. I was prepared for him though, sufficient garrisons in all my bordering cities ready to repel his attacks. A quick peace deal with the Mongolian city-state and a hasty march south later, I engaged the Incan forces and captured one of their cities. By that time, only about a century after Montezuma declared his second war on me, Isabella finished him off, looked around for the closest blasphemer, who just happened to be me, and DOW-ed. I wasn't prepared for her coming after me this soon, and was caught completely off-guard, losing 2 Mongolian cities and one that used to belong to Monty. It was by far the toughest war in that game. Fighting on both fronts, I managed to make peace with Isabella, while capturing 3 of the most lucrative Incan cities. After that, another race up north looking for revenge. A prolonged war resulted in me retaking all I lost, and I managed to get three Spanish cities and raze a forth one as well. My army never left the north in anticipation of a retaliation. Isabella raged, Isabella demanded, Isabella made ugly faces, but another war never came.
However, on the other side of the world Asoka had run away with the game, dominating about a third of his significantly bigger continent and already halfway done with the Apollo program. It was quite the tech race, and seeing that even after constructing the space elevator there was no way for me to win, I sent half a dozen spies over the ocean, who managed to continuously thwart the production of quite literally the last thruster he needed to build his space-ship for probably around 40 turns, until I finally finished my own in 1836.
Not long after I moved on to Emperor (first win with Frederick), for a while played on Immortal as well, but never did I have such an awesome game. Most of what I described happened within 4 centuries of constant warring, backstabbing, amidst political intrigues and religious crusades. I am not a warmonger, but that game was nothing short of amazing in my book, and with a fittingly devious ending as well. Even in its vanilla version the Espionage system in IV was not without its uses
EDIT: Oh, and Tokugawa got beaten to death on his continent, so he escaped on ours and settled exactly on the remains of the Spanish city I destroyed in the last war. I had already gone to two wars with him previously, albeit only on paper to look good in front of the bad boys on the other side of the big water, but I never got around to exterminating him. He was just kind of cute, sitting in his pop 4 capital, looking at everyone else with disdain.
me while I was up north. I was prepared for him though, sufficient garrisons in all my bordering cities ready to repel his attacks. A quick peace deal with the Mongolian city-state and a hasty march south later, I engaged the Incan forces and captured one of their cities. 
