If you are using Adobe products such as CS4/5 you'll definitely want to de-activate them on the old computer before you install the software on your new computer.
I have successfully uninstalled Microsoft Office 2010 from one computer and installed it on another, but I did have to use the automated telephone activation wizard to activate it on the new machine.
When you install the software on the new computer a new Installation ID is generated, which is keyed in using your telephone touchpad and if genuine returns a new Activation ID, which you have to enter to activate your software.