Many people run XP, but may have to do different things to get it to work.
Make sure you have the Patch installed!
Use Win98 Compatibility Mode (as above)
The chances are that your problems are to do with the DirectX/Video System. CC was written before the current generations of accelerated Graphics cards, and many have problems.
Make sure your XP, DirectX, Video and Sound Drivers are the very latest.
You can try adjusting a coupleof things:
Hardware Acceleration (Display Properties...Settings...Advanced...Troubleshoot). Bring it down a notch or 2. If you go down too far, then you risk more problems than just CC!
In addition, use DXDIAG.EXE (File...Run...DXDIAG) and disable DirectDraw.
CC insists in running in 16bit mode. Even if your Desktop is 32 bit, CC will switch it when it running. Make your Desktop the same size and colour as you have CC set to.
None of these is guranteed to work. There may be other causes I am aware of. Let us know how you get on