If, for some reason, you need to change your Unreal Tournament 3 (III) serial number, I have an easy way to do it.
Browse to the Unreal Engine configuration file found at: C:\Users\YOUR_USER\My Documents\My Games\Unreal Tournament 3\UTGame\Config\UTEngine.ini
Open the file, and near the end you will see this header:
Beneath the header lies your key, in encrypted format.
Remove the line that contains the key (in my case: EncryptedProductKey=001000000000208140157etc).
Restart Unreal Tournament III, and it will ask you for your key.
Enter your key again, and presto! You have changed your UT3 cdkey.