Assuming you're using Mail, the app that came with the machine, then all your data should be kept in a folder named Mail in your Home folder's library. If you're wanting to transfer an account to a new machine then simply dragging this folder to the new machine's equivalent location should suffice, although it'll obviously then replace the data on the new machine. If you're wanting to sync accounts then tell us more about your mail setup and we might be able to help.
Okay, well drag the folder named Mail from the old machine's Home Library to the new one's Library when Mail is closed. You may also want to copy across com.apple.mail.plist from the Preferences folder. The great thing about Macs is that you can generally copy a folder (such as Mail, iTunes, iPhoto, Documents and so on) from one machine to another and it'll all work as it used to.