Searched around, found these, maybe they can help.
Although not every problem with Civ4 running can be easily identified, and there is no way to guarantee your problem is identifiable or (easily) solveable, there are several things that can be done to increase the likelihood of fixing your problem!
Links to discussion threads are provided where appropriate. I don't intend this thread to be a discussion thread per se, but simply a reference; please only post if you have suggested fixes that aren't included here.
Edit by Solver. Please note that the official Civ4 1.61 patch is available for download and should be applied to your game.
Fixes for general crash problems
Make sure your OS is fully updated. This means if you run Windows XP, you should be at SP2. Windows 2000 should be at SP4. This is important because sometimes updated drivers don't work (well) with older versions of Windows.
Make sure your Video Card drivers are updated. Both ATI and nVidia are polite enough to provide simple to use drivers that are 'generic', ie work on most or all cards of their brand. ATI drivers and nVidia drivers
Omega: Some ATI cards (and even nVidia cards) have reported greater success rates with the Omega drivers. These are THIRD PARTY DRIVERS that are NOT guaranteed to work with any particular card, and may reduce performance. Back your system up (or set a system restore point) BEFORE installing them.
You also should consider un-installing old video drivers before installing new ones (especially Omega); ATI uninstaller will help with ATI; nVidia suggests you simply use the add/remove programs control panel (which should work for ATI as well). This thread discusses the drivers for ATI and the Omega drivers.
Update your Motherboard drivers and BIOS. Especially with integrated video and sound chips, this can help improve performance immensely, and can solve a multitude of problems. Go to your motherboard's manufacturer (and/or chipset manufacturer) to find the appropriate drivers; there are also many 3rd party sites for this, although not all are safe or recommended.
Here is Intel's site for those of you who use their boards.
Update your Sound card drivers. You would be surprised at how many crashes, even ones that 'look' to be video crashes, are caused by sound cards. Creative's support site for Sound Blaster cards; otherwise go to your sound card manufacturer's website.
Video and Sound system settings. If updating the drivers don't solve the problem, it's possible there is an issue with one of your settings that is incorrectly matching your system, and/or simply not functioning with the game. Examples include:
* Video Settings: AGP related settings have been reported to help (either disabling AGP texture accellerationg entirely through DirectX/dxdiag, or changing the speeds through the BIOS). Access dxdiag through start->run->"dxdiag" and then choose the Display tab.
* Video settings: AntiAliasing has been reported to cause some problems, and is actually often a problem-causer, particularly for ATI cards for many games. Try turning it off through your video card's driver.
* Audio settings: Turn hardware acceleration down or off entirely. This fixes many audio-caused problems.
* Make sure your video card and audio card aren't immediately next to each other (physically) in your computer. The AGP port your video card is presumably in (assuming it's AGP) shares the first PCI port, and therefore if something else important (like the sound card!) is in that first PCI port, it will cause problems under heavy load. It is generally best to leave that first PCI port unused entirely, or at minimum put something low-bandwidth there (like a gameport card, or similar).
* Page file/virtual memory settings: You may want to make sure your page file is set to a constant number (min and max are equal), about 1.5-2x your total system ram. You can access this through rightclicking on My Computer, selecting properties, and then the advanced tab -> performance options button. (Windows 2000; XP should be similar.) If you have 1GB of ram, set it to 1.5GB to 2GB (1500 to 2000 MB), but make sure both min and max sizes are equal.
Make sure you have the right version of DirectX. This means make sure you have the DirectX 9.0c that shipped with Civ 4. If you do have this, then running dxdiag should report on the first tab that your version is 4.09.0000.0904
Try running in windowed mode, or in fullscreen mode. It's possible that one may work but the other fail. You can access windowed mode from civilization4.ini in the \%username%\My Documents\My Games\Sid Meier's Civilization 4\ directory; or in the program file directory under a shortcut called "_civ4config"; search for fullscreen=yes which indicates fullscreen mode; change it to no for windowed, or ask for a popup asking you which to choose at startup.
Clear your game cache every time you change something about the game. The cache stores several files from game to game, and it's possible an old problem could crop up again from these files. Delete the cache folder, and that should help. The cache folder is found in \%username%\Application Data\My Games\Sid Meier's Civilization 4\ directory. Application Data is a hidden folder and you must have view hidden folders turned on (Tools - Folder Options) to see it. Delete the Cache folder entirely (but only when not currently running civ4) and it will re-set the cache.
Restart Civ4 when you start to get problems. It's possible some problems might be caused by minor errors propogating into bigger ones.
Try reinstalling Civ4. It's possible there was an error during installation that re-installing should fix.
Reboot. You definitely need to reboot after installing Civ4 and playing it. It doesn't ask you to, but not doing so causes problems.
Try adding a new user to windows and then installing the game under that user. Often changes you made to something a long time ago, driver conflicts, software conflicts, etc. can break a game. Installing a new user from scratch can get around those (although it may require you to re-install other programs such as DSL/Cable modem programs, etc, under that new user as well, depending on how they installed). To do this (Under windows 2000, XP should be similar).