Shameless Plug: you can continuously backup all your Google email to Dropbox, Google Drive, Box, SugarSync, or SkyDrive via cloudHQ (http://cloudHQ.net). We support txt, html, or eml export. You can also just backup certain types of attachments. And backup is continuous and in real time - as soon as a new email is added it will be transfered and backed up to your Dropbox/Box/Google Drive folder.

Here is a short video on how to setup this: http://vimeo.com/65168186