Gmvault is an open source project that allows users to download all of their emails, as well as the labels.
From there it's as simple as opening them up in a program like Outlook or Thunderbird to view them. It also includes an option to restore the emails.
Most email clients have the capability of doing this, but this was by far the quickest way. Automatic incremental backups can also be done by running a 'quick sync' regularly.