One of my first games had a doozy. I was being attacked by Barbarians, and knowing that Barbarians would pillage my improvements, I moved an Archer out of his city to sucker them into attacking it.
...on Grasslands...one tile outside the city...with nothing left behind to guard the city...
My last game had several though. I had been winning consistantly on Noble and decided to move up to Prince. I'd done so once before already, so I knew it'd take a LOT more to win.
As per my usual tactics, I started the game by sealing off a big chunk of my continent, planning to backfill at my own pace. That pace was significantly slowed by Health and Happiness issues that kept smoke and green clouds over my capital almost the entire time. Eventually, when I was just about finished filling up my corner of the continent - and mired in 4th place (out of 7) - I started looking for where I would put my eighth and final city. I found the perfect spot: a Plains Hill with Gold right on it, and with a Sheep, 2 Fish, and 3 Forests in the city radius.
...4 tiles from my capital
Later in the game, just as Tanks were coming in, I decided that the only way to catch up to Kublai Khan (the leader) was to attack him and take over a big chunk of his empire. He even had a size 12 city that was BADLY losing a culture war to mine, so I could just stack Cannons next to it and take it in a single turn. However, despite the claims of the AI being terrible at warfare, being 3 times my size gave him more than enough units to simply zerg me into a stalemate. I eventually had to give the border town back in exchange for peace because I was about to be overrun by sheer numbers.
It gets better though. As the border town was falling, I sent the majority of my mobile forces - 2 Tanks and 8 Cossacks - to take a city a few tiles in. When I got there, I smashed the defenders down to one badly-wounded Siege Engine while I still had 2 Cossacks that hadn't attacked yet. Knowing I couldn't hold the city if I took it that turn, I did
not raze it...I simply held off until the next turn. This without noticing the little grey lines connecting the city to the rest of his empire...and the reinforcements that would put a dozen fresh defenders in his city that turn and utterly annihilate my assault stack the turn after that.