It looks like both InDesign CS3 and InDesign CS4 are compatible with Windows 7. Here's a press release I received this morning:
Adobe today confirmed that Creative Suite 4 and future versions of Creative Suite will run on Windows 7. Adobe has tested its Creative Suite 4 family of products and components on Microsoft Windows 7 Ultimate edition and found the performance held up to the company's high standards of quality and performance. Creative Suite 3 has also been tested and will support Windows 7 without any updates. Older versions of the software may run on Windows 7, but they have not been tested for compatibility.
Please visit www.adobe.com/products/creativesuite/faq/ for more details.

Thank you for this immediate info I have been wondering about the compatibility.
But how can I install QuarkXpress 8 and Adobe CS3 the last time I did it my CS3 crash after installing QuarkXpress 8
I just installed windows 7 and I am trying to install Adobe Creative suite 8 desighn standard and it will not install. It stops after the first two items install, then the rest show as failed.
What do I do now?
Gilbert Gonzalez