First, I will explain my favorite blogging backup method:
Blogger has an excellent BlogSend feature - As soon as publish a post to your Blog, Blogger will automatically email the entire post to a given email address. To configure your BlogSend email address, go to Settings | Email and enter your email address.
I receive all my blog posts in my GMail account where it automatically gets archived using the following GMail filter:
From: Amit Agarwal <firstname.lastname@example.org>
To: me <a.p..@gmail.com>
Label it "Digital Inspiration Blog Backup"
This way, I have a complete backup of every blog posts in my GMail Archives without using any software or making any changes to the Blogger Template.
BlogSend will only send email to a single address. If you want to send blog updates to more than one email-address, create a mailing list. You can use a service such as Google Groups to do this. Then just enter the mailing list address in the BlogSend setting.
If for some reason, the above style doesn't help, you can try some of these methods:
Create another 'mirror' Blogger weblog that will be a backup of your original blog. Using a blogging software like w.bloggar, post the same article to both the blogs in one step.
Create a exact mirror of your weblog on your hard-disk with offline browsing software like wget, TeleportPro or HTTrack Website Copier. These software create an offline version of the website with similar directory structure that will contain all HTML, images and other files from the server in to your computer.
Modify your Blogger Template to create a single file with all your posts and user comments. Open this file in your web browser and save the file to your local hard drive. Read detailed instructions - How do I create a backup of my entire blog?.