Depending on which application you are using (e.g Lotus Notes/Outlook etc) and how it was set up there should be a file on the PC that contains all that information. Pop onto a usb device or CD and put on to the new machine.
If using Outlook you can save all your emails into a Personal Folders File (.pst) which you can then read in OutlookPC.
You can also create mail Archives from Outlook which work in a similar way.
If you use Outlook Express there is a way to export our mail folders but it's not as easy and I find it difficult to find where the exported files is dumped