Have any of you tried rolling back your drivers? The 71.89 drivers work great for Nvidia cards, all the way up to the 6800GT. Civ isn't programmed to handle the way the newer drivers handle the game yet, so roll them back and you'll solve the majority of your crash problems.
Another tip: Find the directory:
C:\Documents and Settings\'user name'\Application Data\My Games\Civilization 4\cache
Delete these files before running the game each time. (This is basically clearing out the cache) To make things faster, I created a shortcut to this directory and placed it beside my game icon on the desktop. I just double-click, delete everything in it and run the game.
I've gone from constant crashes every 1/2 hour or so, to crashes every 5-10 minutes after I 'updated' my drivers to the latest from Nvidia, to 1 in the last 20 hours of Civ 4 gaming with the new drivers and clearing of the cache. I can't garantee it'll fix everyone's problems, but it worked for me (and lots of others, which is pretty important) so I thought I'd share.
Edit: I should also clarify that my computer ran everything else like a dream, so yes, it isn't your computer and it IS Civ 4. I think its awful that they released the game without it being functional with the very drivers they suggested upgrading to!