Oddly enough applying a no CD fix to the KOTOR will get it to run under Windows 7. My brother had to use this trick to get KOTOR to run under Vista. It seems to work under Windows 7, and it doesn't require you to downgrade your graphics drivers.
You'll need to update KOTOR to v.1.03 (the latest version) first. After that just browse to the directory KOTOR is installed in and replace swkotor.exe with the one in the attached zip file. You should be able to run the game after that.
Just a few notes, though. This will get KOTOR to run, but it will be a bit unstable. Switch swkotor.exe and launcher.exe to XP compatability mode for a bit more stability and
save often, the game will still crash every once in while even under compatability mode. Don't bother with any of the earlier compatability modes. I tried these and the game kept hanging on the load screen right after charcter creation.
If you find a spot in the game where the game keeps hanging/crashing, try changing the processor affinity for swkotor.exe under task manager. You don't have to do this every time you run KOTOR, just if you find a rough spot that keeps on crashing.
If the game runs in a window rather than full screen you can fix this by changing the resolution in Options>Graphics. On my PC KOTOR's option menu gives me three identical choices for each available resolution, I just picked the last one for the resolution I wanted (1280x1024) and game has been running full screen ever since.
One last note. On character creation I found that the game crashes if you try to cycle through the character portraits too quickly. So slow your roll if you don't want the game to crash before you even start playing it

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