I can't speak for others, but I never had any trouble with windows 7 64 bit and illustrator cs3.
The main issues that people have is during installation when they've had past versions of Adobe Programs that were not removed correctly and/or were not the original copies.
If this doesn't apply to you then you shouldn't have any problems regarding Adobe products. I have not heard particular issues with CS3 in Windows 7(I am currently using CS4).
Let me know how it goes.
32- vs.64-bit seems to be a key issue. Please fully identify your operating system.
This is on a 32 bit Win install.
Search yields following hits. Many posters fail to identify whether the problems occur with 32- or 64-bit Windows 7 systems. Many more issues are reported by users of 64-bit Windows 7.