Gmail is having lot of useful features. One of such features is forwarding mails to other mail accounts.
It can be done easily done and it will be more useful for keeping backup copy of your important emails.
For doing this click "Forwarding and POP/IMAP" in "settings" tab. Specify your email address to which you are going to forward the mails. And specify other options also.
Refer this article to know more details.
This feature can be used as mail backup and also it will be useful if you want to read mails from all of your different mails account using single mail client.