I have been slowly working my way up the difficulty chain in CiV. The difficulties are as follows:
1 - Settler - hilariously easy
2 - Chieftain
3 - Warlord
4 - Prince - normal - max AI difficulty - above this the AI cheats.
5 - King
6 - Emperor
7 - Immortal - insanely hard
Most of my games have been on King difficulty and today I just won for the first time on Emperor. I am sure I could have ratcheted up the difficulty faster but I am having a lot of fun playing different civilizations and trying different strategies to win. The tricky thing on the top two difficulty levels is that the AI cheats to an extent that is really shocking. To win today I had to do some really silly things to abuse the AIs strategic weaknesses to eke out a victory, far more than just moving my units tactically or building the correct buildings. By the time I defeated the other civilization on my island and struck out for new territory across the sea the most powerful enemy AI - The Germans - already had an incredible 34 to 23 technology lead on me and their army was roughly 4 times the size of mine. So not only did they have an unbeatable horde of units but they also had drastically better units and better technology. It quickly became apparent that no amount of skill or strategy could allow me to defeat them on the field of battle with their ludicrous advantage so I had to win by going directly for the United Nations and voting myself the winner. Anyone who knows how CiV works will tell you that this is the cheesy way to win as you abuse a huge hole in the AI's logic - they simply wait for the UN vote and vote for themselves while players know that everyone gets one vote from the lowliest city state to the gigantic world spanning empire. I bought the loyalty of a bunch of random city states one turn before the vote and won the game despite being 17 technologies behind and hopelessly outgunned. They call the UN victory the diplomatic victory but really it should be called the economic victory as you get it by having a boatload of money to buy 'friends' to vote for you.
I can see more now why people would complain about this AI's behaviour. At the highest difficulties it is unbelievably overpowered, so much so that no amount of tactics, positioning or cleverness could save the player. The only way to win is to find the holes in the algorithm and abuse them hideously. The computer doesn't cope well with extreme situations as it focuses on building a diversified military so a player can build a 20 unit navy and hold off the computer's 10 unit navy and 60 unit army because of the sea between them. Because the AI enjoys such incredible technology and cultural advantages it is simply inadvisable/impossible to try to defeat it through normal means and the UN vote is the obvious answer since the AI just doesn't quite get how to stop that technique. The unfortunate part of turning up the difficulty is that instead of just playing the normal game better and better you must play the game in a twisted, bizarre fashion dictated by the gaps in the AI's strategies. It is still fun but it surely isn't as good as if we could somehow create an AI to rival the best human players.