I'm facing the same problem after a clean installation,however civ4
didn't crash before as far as I can remember.
The first crash was after building a wonder,the Oracle.No movie,but
a crash.Installing a DivX version solved that problem.
Maybe updating the videodrivers will help,but it can cause a new problem
as it did in my case.
The game did still crash 1 or 2 times during a whole game,so thank
God there is an autosave.