For Outlook on the new PC (assuming it's hooked up to the old one or you
have access to the files on the old one), File > Import and Export > Import
from another program or file > Personal Folder File (.pst) - then browse to
locate the old file and follow the instructions. It'll not only bring over
your messages, but also your address book, calendar, and anything else you'd
been using.
If you want to move the OE messages into Outlook (so you have only one email
program to deal with), then on the new PC: File > Import and Export >
Import Internet Mail and Addresses > select Outlook Express. Then follow
the instructions with your personal preferences.