Go to www.gmail-backup.com/ on your PC computer.
Tap on the DOWNLOAD tab top right of the site and navigate down to the .exe file. Install it and open it.
It should look something like this. It will ask you to put in your gmail and your password. You will also need to choose a date range and a location for the files. Then just tap BACKUP and it starts.
This program stores each email as a .eml file. It can be opened in a word processor like notepad or with an email program like OUTLOOK.
My file which was about 2,800 emails over about 3 years was less than 500MB.
And that is the easiest way I have found so far! It took less than 20 minutes (I have 20mbs internet)
HOW TO DELETE ALL GMAILS AT ONCE:
By request, this is how you delete all the mail in your gmail.
Type either "is:read" or "is:unread" in the search box of your gmail and tap the blue search icon.
Then tap the GREY SQUARE and select All
To select all emails that are either unread or read (other than the emails on the current page) click SELECT ALL CONVERSATIONS THAT MATCH THIS SEARCH. Then just click the trash can.
The .eml file saves attachments and photos!
View your .eml files using MOZILLA THUNDERBIRD.