Outlook Express has an Export/Import feature, under the "File" menu. Simply export the address book to a *.csv file format (choose the fields you need to transfer over, eg. Name, Address, email, etc) and either burn this to a cdrom or (if it is small enough, a 3.5 floppy).
On your new system, open up Outlook Express and use the Export/Import feature to import this file to your address book.
You may have to do some minor editing. I did this recently between Outlook express and Outlook 2002 and it worked great.
I hope this helped.