wpfossil
Chieftain
For me, it was building a Great Prophet while in danger of losing its last city. I did get a free shrine out of the deal though.
The list is endless but a very recent entry had Attila attacking an obsolete city of mine instead of defending his last cities which resulted extinction in 3 turns. This http://forums.civfanatics.com/showthread.php?t=469360&page=4 enlightens the situation with pics (last few out the 9).
G
Carthage, separated from me by a mountain range, declares war and decides it is a good idea to suicide 3/4 of her units while crossing the 2-tiles-wide mountains.
Yeah this happens a bit too often on just about every game Carthage is in. Maybe that's why she never becomes a run away civ in my games. :/
To be honest, given how you have utterly dominated the world by then, I really can't see how Attila could have done better just by defending. Deity AI bonuses or not, by then he couldn't even outspam you even if he wanted. If he waited in his cities, it would only buy him a few short turns before the inevitable collapse.
Him attacking you at this point is more like a last ditch act borne out of hopeless desperation and the threat of extinction.
In my opinion, the pinnacle of AI stupidity is when it tries to get by your line of defense to get to an outlying civ it just DoW'd. This happened to me plenty of times. The AI simply gets his units freaking butchered, and never learns. You can expect the same thing happening 10 turns later
The AI do all sorts of things that seem dumb...like concentrating on your weakest or most vulnerable range unit, when it might make more sense to attack your melee unit that can actually finish off their city.
But having said this, sometimes they do surprise you and will nail that melee unit...making you have to "tread water" until you can get a new melee unit up to the front.
Hmmm, I sometimes wonder if they "know" that it will buy them time if they take out that melee unit.... But, I suspect not...