Google has always made it rather difficult to export email from Gmail, but that's about to change. Google is adding an option that enables you to export your whole email account (or any mail with a particular label) in MBOX format.
The option is accessible by clicking on the Account link under your photo in the top right corner and then choosing 'Download your data'. As with many a Google implementation, this going to take a while to roll out — Google says as long as a month for some users. Even if you don't plan to leave Gmail, having the ability to easily backup data is a welcome change.
Download a copy of your Gmail and Google Calendar data [Official Gmail Blog]