Not really the 'worst military disaster', but I am in the process of getting unexpectedly screwed at the moment. I decided to backstab Willem of France, my most friendly civ on the continent, while he was in the middle of a war with three other civs. His land spread from east to west, mine was a north-south pillar that touched upon the middle of his land, pretty much.
I decided to attack from two angles, coming in from the north of both ends of his empire. I had two nice big stacks that could comfortably stomp through his cities with only a couple of catapult suicides for casualties, give or take. It was going fine, my eastern attack force was having no trouble whatsoever, had taken a couple of cities, likewise the western force, they'd taken two as well, including Paris. But this is where it all went wrong. I'd left about 10 units, including 5 full strength longbowmen and crossbowmen, in Paris while the rest went about their main objective. They'd moved south-west towards another of Willems cities, and just as they were bombarding their target, a French stack appeared right outside Paris. It wasn't enough to take it back, really, but I thought I'd play it safe and send a few attackers back to help out.
Willem attacked Paris with five elephants and a couple of cavalry, and amazingly managed to kill seven of my untis. I looked at the combat odds afterwards and the odds of loss in order were roughly 8%, 10%, 10%, 20%, 25%, 40%, and then a weakened unit at around 60%. And that was it, it completely changed everything. Most of the crossbowmen and longbowmen were one XP away from an upgrade, which meant healing, and with a medic archer in there things would have been fine. This lack of defense meant they could capture the city back before my attackers could get back to defend and then they moved some longbowmen in there. I decided to send more attackers back to recapture, but they then just moved a stack to my newly captured city and beat up my weakened, fractious attackers en route thanks to their recaptured roads, and they're casually destroying my forces outside Paris now.
I went from a minimum power ratio of 2.0 on this continent to 1.6 in about five turns. I've got reinforcements coming in dribs and drabs, and I can still take his empire fairly comfortably when the eastern force arrive, but my God did that bad luck slow things down.