You can certainly copy your iClone content from your old computer to your new one. To do so you will need to transfer it directly over a network or use a flash drive or DVD.
Basically you will want to copy over the iClone Template folder if you have any purchased content packs and don't want to install them all over again. You will also want to copy over your custom content folders for any work you have created yourself.
To complicate matters a little, since the release of the iClone 4.1 update, your iClone template folder will have moved to new location. If you look below you will see the general locations you will be able to find all your content.
The folders marked in red are the ones you need to copy over depending on your Operating System.
In the past, the iClone4 Template folder will locate at the following position:
X:\Program Files\Reallusion\iClone 4\Template\iClone Template
We updated our program file location since iClone4.1. You can find the files in the following locations:
iClone4 Template folders: (Windows Vista/Windows 7)
X:\Users\Public\Documents\Reallusion\Template\iClone 4 Template\iClone Template
iClone4 Template folders: (Windows XP)
X:\Documents and Settings\All Users\Documents\Reallusion\Template\iClone 4 Template\iClone Template
iClone4 default custom folders: (Windows Vista/Windows 7)
X:\Users\Public\Documents\Reallusion\Custom\iClone 4 Custom
iClone4 default custom folders: (Windows XP)
X:\Documents and Settings\All Users\Documents\Reallusion\Custom\iClone 4 Custom
(where X is the drive letter on which iClone4 has been installed)
Just copy the folders to the exact same location on your new computer.