Had a game a quite recently with two real stand out moments of AI stupidity. The situation was this: decent sized continent with five people on it: Me (Asoka), Isabella, Monty, Sitting Bull and De Gaulle. Izzy founded Christianity early on (Choose Religions was on) and it quickly became the dominant, and indeed only, religion on our landmass.
The first piece of monumental stupidity came when Monty decided to start his first war. He shared borders with everyone but me, and the power levels, apart from him being well ahead, were pretty even. IIRC, he hadn't found metal or horses, so it was just solid Jaguars. So who does he pick as his prospective victim? Yep. Sitting Bull. I was watching it with a scout, and he must've suicided about 50 Jaguars on one of SB's cities that was not only defended by Dog Soldiers and Protective, +3 exp Archers, but was on a hill.
Eventually, he gave up, but only after giving SB some level 6-7 archers and Dogs, plus a couple of GGs.
The second event of note came when Izzy was the first to research Theology, and founded Judaism. At this point, Monty was rebuilding his armies, Sitting Bull was, well, sitting in the corner not doing much, De Gaulle was stuck up north with a bunch of Tundra cities, while me and Izzy were pretty closely matched as the top civs, roughly 50% higher than the others.
As I said earlier, Christianity was the only religion on our continent before this - the others were founded overseas - so there was a nice bit of religious love going on. Nothing much happened at first, until Izzy popped a prophet and built the Temple of Solomon. She then, pretty sensibly, decided to spam Jewish missionaries. About a dozen turns later, De Gaulle suddenly adopts Judaism. Yes, you heard that right, he chose to switch to a religion where he'd have no allies, yet four enemies, including Monty and Izzy. It wasn't even the main religion in his cities (he had about 5 with Judaism, compared with 7-8 Christian ones).
It took about a dozen turns before Izzy declared, and Monty, unsurpsingly, jumped in too, even dragging his former enemy SB in with him.