You can install this module:
https://bitbucket.org/jlaloux/website_noodoo
This module removes "Create a free website with Odoo"

I commented it out using the CMS website editor.

Customize -> HTML Editor -> Main Layout

That is where I found this code & added <!-- --> 

<!--Create a <a href="http://openerp.com/apps/website">free website</a> with <a class="label label-danger" href="https://openerp.com/apps/website"> OpenERP</a>-->

Note: I am using v8dev pre RC1, your mileage may very.

1. Log in to the Odoo admin as administrator. Activate Technical Features, if not already activated, by going to Settings > Users > Users > Admin > Edit > Usability > Technical Features > check the box (on), click Save.

2. Go to Settings > Technical > User Interface > Views.
In the search box, next to filter icon, type "Footer Copyright", and hit enter to search.

3. It will show: View name: Footer Copyright. Click to open it. Click Edit.

Comment out lines of the code as follows:
<-- Powered by <a class="label label-danger" href="http://www.odoo.com/page/website-builder">Odoo</a>,
the #1 <a href="http://www.odoo.com/page/e-commerce">Open Source eCommerce</a>. -->
Click Save.

4. Refresh the browser view of your Odoo front end website. Log out and try to logi in again. The previously visible "Powered by" backlinks and text, are gone.

Congrats.

Customize -> HTML Editor -> Brand Promotion (For Odoo v12)

Just to clarify number 2: Go to Web Page, Customization, HTML/CSS Editor

Editing this through the html editor under the 'footer copyright'  only works momentarily but once you sign out - it comes back up again. OR if you go and update the Website module and go back to sign in it all resets to how it was!  The only way to get rid of this is to install the module that was refered to by Julien Laloux above.

Another way to get rid of it is editing the website module. but i prefer the custom module above.

1. Log in to the Odoo admin as administrator. Activate Technical Features, if not already activated, by going to Settings > Users > Users > Admin > Edit > Usability > Technical Features > check the box (on), click Save.

2. Go to Settings > Technical > User Interface > Views.
In the search box, next to filter icon, type "Footer Copyright", and hit enter to search.

3. It will show: View name: Footer Copyright. Click to open it. Click Edit.

Comment out lines of the code as follows:
<-- Powered by <a class="label label-danger" href="http://www.odoo.com/page/website-builder">Odoo</a>,
the #1 <a href="http://www.odoo.com/page/e-commerce">Open Source eCommerce</a>. -->
Click Save.

4. Refresh the browser view of your Odoo front end website. Log out and try to logi in again. The previously visible "Powered by" backlinks and text, are gone.

 

Congrats.

Customize -> HTML Editor -> Footer Copyright for v8