depends on what event it is and what the situation was.. my current game i when I had settled my second city, I tried to boost production by building mines on the hills, my mines got destroyed by random events the turn after they were built, even had it where it was destroyed and a forest grew over it because my worker wasnt there lol.
Another bad event.. I was hit by Monsoon and my granary was destroyed, then I was hit with other bad weather and my farms and pastures were destroyed. Then, I got the Vermin in the food stores. my capital starved making tthe pyramids lol.
Few other bad ones are the raging barbarians that show up at your door step when your about to goto war. I rush to the Great wall so barbs dont bother me unless Im at war early i nthe game and my units are crossing thru the fog. but that slaughtered half my units, so I had to stop heal, and bring more.. but the Greeks showed up before reinforcements.
Another bad time was I had the raging Barb one again, and I decided I'm gonna wait it out, then I seen the message again, Mansa Musa got them.. There were two Stacks of barbs now between my territory and Mansa's and.. well he got a few cities taken a way and i used that to my advantage. and claimed them.
Few other bad ones are when your egging someone on to fight so u can pul lthe defensive pacts in rather than recruit during war, then a random event says they were nice, so It increases relations decreasing the chance of war lol