Here is a good Windows software option, called MailStore Home, that you can use to download and backup your Gmail. I can also see using this to archive a Gmail account that is getting full.
MailStore Home is a free email archiving and email backup software for personal use.
With MailStore Home you can backup all emails in a central archive, even if they are distributed across different computers, programs or mailboxes. You can do this either on your PC or on a USB drive as a “portable” option.