According to the FAQ, both CS3 and CS4 have been tested and confirmed to work with Windows 7 Ultimate Edition, without the need for any patches. Compatibility with the Home Premium and Professional editions of Windows 7 has not been tested. Depending on the editions of Windows that the computer is upgraded from and to, the upgrade process may require reinstallation of Adobe CS3 or CS4 applications using the same procedure as when they were originally installed.
There are a few points to note, however. The company does state that customers will find Adobe's software trials end prematurely if they upgrade to Windows 7 after starting the trial on a previous operating system. Customers using third-party plugins and hardware with CS4 are advised to check with the manufacturers to confirm whether they're compatible with Windows 7, and some Creative Suite users may find that after upgrading they aren't able to use GPU acceleration features until an updated graphics driver is supplied.
Customers using older versions of Creative Suite are advised that they haven't been tested on Windows 7. Hence they may or may not still work, and won't be supported or patched for Windows 7 compatibility regardless.
More details can be found in the Adobe 'Support for Windows 7' FAQ.