I usually play at Civilization IV with difficulty set to Prince, length set to Marathon and size of the map to Huge.
The problem is that happens quite often, in the 20 century, that an opponent win the game by reaching the Cultural Victory.
How can I understand that an opponent is going to win in this way and what can I do to impede his/her victory.
Best Answer
If you go to the Victory Conditions screen (I believe it is F8) it should show you what is required for a cultural victory based on your game length. The left hand column shows how close you are to each condition, but the right hand column should show which of your opponents is closest. So you can watch this to see if they are gettting close to a cultural victory, and if so, attack the cities as mentioned in the other answers.