Post updated on 4 July 2013.
How do I remove the Powered by Blogger from my Blogger blog in the new blogger interface?
In order to remove you will need to edit the blogger template and delete the attribution widget in the new Blogger interface.
If you are using the old interface, please read this post on removing Powered by Blogger in old Blogger interface.
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Please backup your blogger template before you make any changes to it. This helps to revert back to the original template when something goes wrong while editing your template. The steps for backup and restore are discussed here in detail.
Steps to remove the Powered by Blogger text from your blog in the new Blogger interface:
1. Click on the Template link in the left navigation menu.
2. Click on the Edit HTML button
|Remove Powered by Blogger|
3. Search for Attribution1 inside the template. Delete the highlighted line as shown in the image and click on the Save Template button.
Update : Video - How to remove Powered by Blogger
Update: How to remove Powered by Blogger in mobile template?
Follow the above steps and select the custom option in Template.