Perhaps you are changing jobs or you have decided to discontinue using an email account. Or maybe you simply want a copy all of your emails in case something happens. No matter what reason, it is a good idea to backup and export Gmail and other Google accounts via Google's Takeout service. You can actually set up your accounts to backup regularly which is a good practice.

Note: If you are backing up an account for a company, it is possible that Takeout has been disabled by your company. You can backup your Gmail using third-party apps, but make sure to check the policies of your company before you use them.

HOW TO BACK UP GMAIL
Go to Myaccount.google.com
Click on Privacy & Personalization to access "Manage your personalization & data."
Scroll down until you see "Download or Delete Your Data." Click on "Download Your Data."
This will take to you to the Google Takeout Page. To download only your Gmail account, click the "Deselect All" button at the top.
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Scroll down to Mail under "Select data you wish to include" and click the checkbox (along with any other apps)

After it has been checked, you will see two buttons. The first button is called "Multiple formats" -- click that button to view the format in which your data will be saved. If you are only interested in downloading specific categories, the other label will be "All mail data included".

Scroll down and click on "Next step."
Click the arrow under "Delivery method" and you will see all options. You can email a link, add it to your Drive or Dropbox, OneDrive or Box.
You also have the option to choose to export once or twice a month (for up to one year), as well as the file type and maximum file size. If the file is larger than the maximum size, it will be split into multiple files. Files larger than 2GB will use zip64 compression format. After you're done making your selections, click "Create export."
Google Takeout settings
This section will show you the options to export your data.
The export process will begin. It may take several days for your export to complete. You can click "Cancel export" and "Create another Export."