I just recently got a new MacBook Pro, migrated my data over from my old laptop with Time Machine, and upgraded to Snow Leopard. Everything worked great, except Fireworks CS3, which wouldn't start and spit out the message: "Licensing for this product has stopped working".

After a couple hours of fiddling around and troubleshooting, I finally came up with a solution:

On the old laptop:
  1. Open Fireworks and go to Help -> Deactivate...
  2. Complete the deactivation process.
On the new laptop:
  1. Uninstall Fireworks.
  2. Move the "/Library/Application Support/Adobe", "/Library/Application Support/FLEXnet Publisher" and "/Library/Preferences/FLEXnet Publisher" folders somewhere else (you probably should keep them around somewhere just-in-case everything goes bad).
  3. Install Fireworks.
  4. Open Fireworks. It should ask you for your license key, and work!
Hope this helps someone else save a few hours of frustration...