I rarely pay much attention to the Victory Conditions as given, since I care less for how the game ends than for how the game proceeds. So, I set 'in game' victory conditions for myself.
Examples:
Play Xenophobic China: not only build Great Wall across the border with, say, a Tundra full of barbarians, but Never allow Open Borders with any other Civ in the game and massacre any Missionaries crossing the border. Result: the original Hermit Kingdom concentrating on all internal resources rather than Trade - it's surprisingly difficult to get a decent Empire going that way for any length of time.
Play Cornucopia of Excellent Goods At Reasonable Prices: try to maximize the trade routes and trade route income, regardless of anything else in the game. My previous record was with Scythia, of all people, but I'm preparing to start a game with Dido and see how much I can beat it with the new emphasis on Sea trade routes.
Transcontinental Railroad. My latest. Playing on a Pangaea Map with Roosevelt, my sole purpose is to build a railroad from one side of the continent to the other, coast to coast. So far this has required that I seize a Canadian city that was in the way, kill Georgia completely (their capital blocked the only direct pass through a mountain range: so sorry for Tammy) but otherwise have largely managed it peacefully. Also had to rename a couple of cities so that San Francisco was available for the city on the far western coast. . .
I play most of my games with the Mods Faster Starting Settlers and Expanded Initial Vision and so frequently start my games as a Nomad - moving my settler for a turn or two before settling down. This is not always strictly necessary from a gameplay standpoint, but for almost all the given Civs in the game, it's more historically realistic. I can't wait for the Mod Community to modify the Maori start to land-based Civs like the Huns or Commanche or Goths, so that I can do some Real nomadic starts. . .
I name cities according to where they belong - can't stand the idea of, say, London being land-locked or Saint Louis being on the sea coast. And I name units constantly, either to give them historical flavor or whimsicalyl. I have a couple of times recreated the WWI British 'I' class Battlecruisers by naming Victoria's Battleships, but instead of the Indomitable, Invincible, etc. I use HMS Insipid, Inconceivable and Incontinent.
And, being a writer of military history of the Soviet Union's forces in World War Two, I've been known to rename cities in the game, so Peter's Sankt Petersburg becomes Leningrad, and the Soviet cities Kalinin, Gorkyi, Kuibyshev and Ordzhonikidze appear on the map.
- Oh, and Vladivostok is always the farthest Russian city on any of my maps from the Capital, just for grins.
None of which has the slightest thing to do with any 'traditional' way of playing the game, but it keeps me interested.