I was using Eudora for email on my Mac. I just activated the Apple Mail application and now I can no longer receive new messages in Eudora. I can send, but not receive. I get an error message alluding to password error. I can read the new messages in Apple Mail, but prefer Eudora. Can I uninstall Apple Mail?
Open up Mail.app, and visit the preferences (Menu Bar>Mail>Preferences).
Change the default mail client in the drop-down menu under "General" to Eudora.
If you really wanted, you could just drag Mail.app from your Applications folder to the Trash at that point, but I would just leave it and ignore it.