Serial number storage is entirely up to the individual manufacturer to store and either allow or not allow retrieval of. Sometimes they only store the hash of the sn for comparison on your local network or online activation, and don't have any way to recover the entered number.
It's also somewhat common for products to only display most of their sn, not the complete number, so you can (as an admin) determine which serial numbers are on which machines, but a user can't pull up the full number and copy it and take it home to activate his copy on his pc.
In many cases someone has written something to recover the password. The most well-known of these is "magic jellybean", which is used on a windows computer to recover the full windows and ms office serial numbers from the computer.
I don't know anything offhand to do this for adobe software. It may not exist because its not possible to do.
I work for the Department of Redundancy Department
This worked for illustrator but not photoshop. Are they the same serial number if a cs was installed rather than photoshop alone?
Interesting. In my copy of CS3 both Illustrator and Photoshop have their Serials listed under System Info. And they are NOT identical, albeit close: my Photoshop serial consists of Illustrator’s serial 16 digits, plus 4 more. If you have trouble digging through the data in the System Info window, copy its contents with the handy button, paste it into TextEdit and run a search for ‘serial’.