Just chipping in to confirm that the game WILL work with Windows 7 x64. I have it installed and have played both skirmishes and campaigns and had no crashing or stability problems.
I didn't have to use any compatibility modes or change any settings to get it to work, either. Have you tried patching Tiberium Wars to the newest version? I did that before I started playing (mostly for bug fixes, to be honest) and that could be why it works for me and not for you.
Are you using the Expansion (Kane's Wrath) or just the vanilla version? I also do not have the expansion installed, so that could be why mine works and yours does not.
I'm running version 1.09, and you can download the patch here
Hopefully this will help you out.