I rolled a random game (random map/leader, standard speed, standard map size) and landed Ghandi - immediately deciding to take my first real run at a Cultural victory. Started out my coastal capital, explored a little and found an aggressive Askia very close - along with Arabia. Having established city #2 (production) and having had Askia laugh at my military 'might' I stepped up a notch when i found iron, and went at him with swords/archers. He was quickly wiped out, and puppeted, along with the Arabs too. So far so good, with my capital growing like crazy and a Trade-Post strewn 'continent' thanks to the numerous worker captured.
For some reason I never got around to fully exploring via land, but had sent a trireme out (nothing beyond that as I was focussing on Culture Building overkill, and a decent defensive army). It was late in the day then, when I finally realised that I was on the Americas map (and had bascially taken total control of North America) and that the south was shared between 4 or 5 Civs with Alexander dominating (it was only when I teched satellites that I would realise that France were also in the game, and of a decent size, but by then my 'moment' had come and gone)
Having established that it was the Americas map I decided to send a force down the landbridge to block off Alex's potential to expand northwards - and I discovered that Siam had kindly built a city right around Panama. I declared and took it off them, quickly establishing it as a giant fort (complete with GG stronghold, doubtle artillery, etc). I was happy to leave it at that, and concentrate on my cultural win, but Alex had other ideas, and bought off all of my CS allies a turn or two before DOW - including two of the three in my northern continent (seriously, he had around 15k gold in the reserves and I lost 4 allied CS in a turn!)
From my 'Panama' base I was able to see his nearest two cities, and effectively stop anything from surviving more than a turn in their vicinity. Eventually he offered peace, which I took but with a plan in mind. To be fair victory was all but assured, but my income was huge (something like 300 GPT out of GA - and I was in almost a perpetual GA chain by then - and around 13k in reserve at that time from chain selling luxuries to all of the underdogs) and I had nowhere to focus it....
...so, with 5 turns until my final policy pop, having built and rebased two nukes, I DOWed on Alex and proceeded to nuke his cities and bombard anything within sight, once the Utopia Project was underway I annexed 'Panama' and spent 14 turns buying a Nuke plus 5-10 guided missiles every turn, and launching one after another into any patch of revealed map I could see, whilst also dumping 4 destroyers and 2 SAM sites for his suicide fighter raids... just for giggles.