It was trivial in the long haul, but I remember one time a veteran spearman fortified in plains took out four of my veteran cavalry. Three redlines and a kill later, the spearman was a redlined elite. That means he had gone 12-4 in combat rounds against 1:2.2 odds. I don't know the math to figure out exactly how unlikely that is, but let's just say the RNG was pretty unhelpful. I probably wouldn't remember it except the stupid spearman was in a key location I needed to break through, and delayed my war by an entire turn as the reinforcements had to be brought up.
I remember one other time I was staging for an attack. The main route was jungle with no roads, so I sent my cannons and "slow-mover" escort around the flank to join up with the main attack later. I declared war and moved my main force into the attack, but the very next turn, just before the canons got to my intended route, an intervening Civ's borders expanded, and when I tried to go through anyway, it was "Move or declare". So I moved, intending to go further around the flanks. The turn before I got through that route, the same Civ's borders expanded there, too, and again it was "Move or declare". By the time I got a road built back at the original entry point, the war was pretty much over. I gained only about half the ground I intended, just because I couldn't get the darn canons through.
Of course, I should have just brought up a big enough stack of workers to build a one-turn road, but I didn't want to pull them off other tasks. So is that luck, or bad planning? I prefer to call it bad luck, but I know what I'll do next time....