I used these instructions, but the Ubuntu One Music icon is still in the dash.
This has changed from previous versions where all you had to do was
sudo apt-get remove unity-lens-shopping
However that does not work with 13.10 (and presumably later versions when they are released).
Ubuntu 13.10 does not have the shopping lens any more but now has Smart Scopes instead.
To disable a dash plug-in, From the dash select filter results then "Dash plugins"
To disable a plugin, click on it and then click the "Disable" button. You can re-enable it later if you want.
You can also disable all these plugins from the command line with
gsettings set com.canonical.Unity.Lenses disabled-scopes "['more_suggestions-amazon.scope', 'more_suggestions-u1ms.scope', 'more_suggestions-populartracks.scope', 'music-musicstore.scope', 'more_suggestions-ebay.scope', 'more_suggestions-ubuntushop.scope', 'more_suggestions-skimlinks.scope']"
Source here:How To Disable Amazon / Shopping Suggestions And Other Unity Scopes In Ubuntu 13.10
This stops the scope running but does not remove it from the dash
If you want to do this first unlock it from the launcher by right clicking it and selecting "unlock from launcher".
You will still be able to search for it in the dash but you can remove it from there too.
You need to run nautilus as root to do this See my answer to this question Why is gksu no longer installed by default in 13.04? for instructions on installing gksu or a workaround to run GUI apps as root.
You can now run the file manager with gksudo nautilus
Naviigate to /usr/share/applications find the file with the amazon logo and delete it.
Finally reboot and its gone for good.
I am not sure about the implications of this solutions but after removing shopping lens from Ubuntu 13.10 and higher (presumably)
sudo apt-get remove -y unity-lens-shopping
and disabling the scopes
as well as disabling remote search (this way your searches won't be sent to some remote location)
gsettings set com.canonical.Unity.Lenses remote-content-search none
you can also manually remove the link from dash ( please comment if this is the correct way or there is a better way of doing this )
sudo rm /usr/share/applications/ubuntu-amazon-default.desktop
This command lists all the scope files that can be disabled:
find /usr/share/unity/scopes/ -name \*.scope -printf "'%P',"|sed -es':/:-:g' -e's/,$//'
There are some scope files missing in the above command like 'code-manpages.scope', 'grapics-openclipart.scope', 'video-remote.scope', 'video-local.scope', 'help-yelp.scope', 'reference-zotero.scope'
All you need to do is open the GUI of your home folder, go to system and search amazon. You will then see all the amazon files on the computer. They will all have a lock icon on them, so to delete them you must go into your terminal enter sudo su, then enter you password. This makes you Root which will allow you to delete these files. From there you right click each amazon file find the directory they are located in. in terminal once root do cd (copy and paster the directory of the file's you want to delete) once you enter that directory do rm (that file). all the information to do this is in the GUI when you right click each file.
How can I disable Amazon search results in the Unity dash?
Click on the Ubuntu button, search for "Privacy" and then turn off "Include online results" :
You can also remove it entirely by clicking on this button, then the orange "Available on the Ubuntu Software Center" button and selecting uninstall:
or via the command line
You then need to log out and back in.
Another option would be to move the lens entirely out of the home dash and make it a standalone lens:
If you don't want online shopping results in your dash but there are times when you want to search the Internet from your queries (for example, while using the Askubuntu scope to the help lens), you may not wish to disable the "Include online search results" item. In that case you may wish to remove particular packages.
For the new dash home lens (default) queries that are forwarded through Canonical to Amazon uninstall unity-lens-shopping.
Either click on the bag icons above and click the Remove button on the right in the Software Center window that appears, or use an alternative of the following command line after bringing up a terminal with Alt+Ctrl+T.
Or, launch Ubuntu Software Center, click Installed, expand Themes & Tweak, and scroll to the its end. You'll see Shopping lens for unity there (along with a lot of complaints).
For the already existing video lens lookup you can choose the source of searches by using the "Filter Results" item on the top right, and then selecting the sources you want by using the Sources drop down. Alternatively you can uninstall unity-scope-video-remote.
Either click on the bag icons above and click the Remove button on the right in the Software Center window that appears, or use the following command line after bringing up a terminal with Alt+Ctrl+T.
sudo apt-get remove unity-scope-video-remote
As in existing releases, online shopping for music in 12.10 can also go to the Ubuntu One Music Store. To remove that feature click on the bag button for unity-scope-musicstores and click on the Remove button on the right in the Ubuntu Software Center window that appears.
or enter the following command in a terminal:
sudo apt-get remove unity-scope-musicstores
In addition to the other answers, you can also redirect the queries to another location by changing the URL it uses for the product search:
echo 'OFFERS_URI="https://localhost:0/"' >> /etc/environment
And then restart your session.
With Privacy Indicator you can quickly enable or disable online results:
IF you want to have a Ubuntu LiveCD without Amazon stuff there is a remastering script: http://www.helplinux.ru/wiki/en:kb:make-ubuntu-safe
Update: if you want to have a Ubuntu LiveCD with disabled online search results by default there is a new remastering script for this: http://www.helplinux.ru/wiki/en:kb:make-ubuntu-privacy-friendly