You will find the "Powered By Blogger" attribution gadget in almost all the blogs you host on blogpsot. By default its locked and can be removed with some minor tweaks in the template's HTML code.
Steps to remove the attribution gadget from Blogger:
1. Log in to your Blogger Account,
2. Go to -> Template -> Edit HTML -> click on Proceed.
3. Make sure the "Expand Widget Templates" check-box is checked.
4. Search the below code using Ctrl+F:
<b:widget id='Attribution1' locked='true' title='' type='Attribution'>
5. Replace it with the following code:
<b:widget id='Attribution1' locked='false' title='' type='Attribution'>
6. Click 'Save'.
Go to the layouts tab, open the Attribution Gadget located at the bottom by clicking edit link. You will see a remove button which wasn't there before you modified the code. Click Remove and it will be gone.
Now, wasn't that simple?