I am sure you all have had CIV situations where you go /facepalm because of weird AI behavior about Open Borders.
Here's a list of my favs, sorted for idiocy:
#5 OB idiocy:
Toku, as usual, refuses OB. Two turns before I win a time victory he comes running and ask for OB. Interestingly, we are both land-locked civs on separate continents, which in the scenario I played are separated by an impassable mountain range from pole to pole.
#4 OB idiocy:
Hatty and I have a pretty involved border fight - her extreme culture is threatening my only copper and ivory, so I am building culture to counter her. Resulting dislike is enormous. Perhaps I should also mention that she thought herself strong and made demands (which I refused), attacked, got smashed, got counter-DoWed, etc. So the mood is BAAAAAD! Me hate her, she hate me - I think we were at -12 or so. Beyond her is Monty, then Toku and Bizzy. All three declare war on me, and since I can't get at them (me sea routes are also blocked by Egypt!) I can only sit and wait for their attacks. Then, suddenly, Hatty pops up and asks for OB! I am her worst enemy, and she hands me my saving grace on a silver platter! :doh!:
#3 OB idiocy:
I have been aiding my friend Bizzy in his war against Cathy. To get to the front my units must pass his territory. He cancels OB.

Ten turns later he lost 4 of his 6 cities and came running to me as a willing vassal!
#2 OB idiocy:
I slaughter the Maya. My SOD takes razes five (jungle) cities and gets so close to the capital, with Pyramids in it, and OOPS! I missed a galley! There's now two chariots ready to attack my capital that has a lone axe in it.

I sue for peace and get it, but my stack is teleported to a little peninsular on the other side of the Maya. Now, they have an ally, Monty, and he is on my other side. Fighting hard, really not giving ground and always dangerous with his woodsman II jags. So I
need my SOD, and I need it
home.
Two turns after peace I get OB from Pacal!
and the #1 idiocy with regards to Open Borders:
Justy and Monty have been having a go at each other for ages. They started fighting at about 1500BC and are still at it in 400 AD. Axes, archers, Jags, you name it. Why neither side has macemen, or at least catapults - well, war's bad for the economy (hear that, Dubya?). I sat by and watched, but then the pesky English attacked me, as did Toku, so I took their countries over. And now, suddenly, there is my territory in between the two warring maniacs. Justy has no problem, he took OB right when I discovered writing. Monty, on the other hand..... So ha has that Jag caught in neutral lands enclosed by my borders, who is constantly running the gauntlet of passing Byz stacks. And he get clobbered at home, because he builds attackers like crazy but must defend only. I deal with him a lot, techs, res, gpt. But he will not accept OB. Oh well, your problem!
After about 30 more turns of this, HE DECLARES WAR!!!!!!!! I sit back and watch - level 7 maces and pikes, backed by Knights, can deal with anything he has. And all he does is
march his Jag home! Once the guy is in Monty's borders, he is willing to take peace for peace

He risks a war against a civ that has 3000 points to his 459, has maces and knights to his ancient era units -
just so that he can get 1 unit home without giving me OB!
Now tell us your fav AI OB moron moments!