Morrowind Connect

I take no credit for the information contained here. I have only tried to assembled it in one place so as to make a more helpful troubleshoot.
I also will not be responsible for anything nasty that happens to your computer as a result of any advice or tips.

Step by Step CTD troubleshooting
Known Issues and Resolutions

Morrowind is a great game but it can be a pain sometimes.  It is a CPU hog and does not like other applications running in the background.  Specifically virus software and 3rd party programs.  Before starting a game make sure to turn these things off.  Most Microsoft services are okay unless they are memory intensive.  If you are having problems a good place to start is with a DXDIAG. 
Post it here in a new thread (don't start another thread if you continue to have problems use the same thread).

Installing Morrowind
When installing Morrowind and the expansions, make sure that you install Morrowind first, Tribunal second and then Bloodmoon, then the  Bloodmoon v1.6.1820. patch.      If you have a GOTY version you will not need a patch as is is already done.
TES Patches

Video Card Issues
Sometimes newer isn't better. Here is a list of the supported video card's and minimum system requirements when Morrowind was released.  This is not to say that newer cards won't work. Most of the time it reverting to an older driver will fix the problems.  This info is contained in your DXDIAG. The people that frequent the hardware and software section are very helpful. If you are trying to change a driver use Driver Cleaner Pro after uninstalling your current one. Then install you new driver
How to Properly Update your Video Card Drivers.

Codex Issues
Morrowind does not like certain codex's. A full list has never been compiled to my knowledge but many of them are known like intervideo.  Nightmare3012's Codex Reset Utility will reset them to the Microsoft defaults. Follow the instructions in the readme. 

High Page File
Your page file is basically the programs that are running all the time/at startup.  This info can be found in the System Information Section of you DXDIAG.  As a general rule of  thumb the lower the number the better 150 to 200 is a reasonable number.  If it is higher than this you should perform a Clean Boot. Here are 2 other tools to manage you start up list.
StartupList 1.52.1
StartUp Manager

BSOD'S
Otherwise known as the Blue Screen Of  Death.  This can flash by rather quickly and sometimes you need to copy the information down. 
Read here to learn how to  disable automatic reboot.
BSOD Troubleshooting

Memory Issues
If you are getting multiple CTD error and multiple BSOD error messages, there is a chance you RAM may be bad. Two tools to check this are...
Memtest86
Memtest 3.5

Hardware
Need to know what hardware you have in you computer Everest Home Edition is the tool you need.