At the beginning of the availability of the CS3 beta, there was all kinds of grief getting the beta working with an acceptable serial number. Some tried using their CS2 serial, which doesn't work. Others used their CS2 serial to generate a CS3 number from Adobe's website, but they didn't always work.
Then there are those folks in education who have blanket corporate serials–once one person used it to generate a CS3 number for their workstation, the rest in the system were out of luck ("number has already been used"). To my knowledge and in my own experience, this has not been resolved–or if it has, Adobe has not yet bothered to tell me in response to my forum posts and email requests.
Check the
Adobe CS3 forum and search for "serial" to view the relevant threads.