One of the oldest idea I am using to take backup of my Gmail emails is to download them to computer. But the small question is how to? There is a small utility of program that you can download and install. It is only 4.4 MB program and takes only seconds to install. After downloading and installing this program you can open it or start it, you will a application window as you can see it in screen shot.
In login field your full email address of Gmail and in second field your Gmail Password. In third field you can choose your directory where you want to keep your downloaded emails.
This program is very easy to work with. If you face any problem while working with program let me know.