If you made new folders to organize your e-mails, go into the directory where you installed Eudora and look for the directories (not files) with the *.fol extension. Just copy the entire *.fol directory to wherever you wish to back it up to and then delete it.
If you ever wanna re-read those e-mails, just copy the *.fol directory back into where they came from originally. But you can only do this if you haven't named a new folder with the same name. This isn't really a problem though since you can rename the *.fol directory name and Eudora will recognize the change.
Also, if you only wanna copy specific mailboxes, go into the *.fol directory and then copy the respective *.mbx and *.toc files for the ones you wanna backup. Or if you haven't made separate folders, you can copy the *.mbx and *.toc files from Eudora's main directory.