That really depends on the mail server/client. For Outlook, you can easily backup the pst file. Mailinabox, you can backup the entire folder structure. Gmail

That really depends on the mail server/client. For Outlook, you can easily backup the pst file. Mailinabox, you can backup the entire folder structure. Gmail still lets you download an archive. There is always an option to print to pdf, and save each pdf offline.