For 12.04
You can use dconf-editor
to rearrange the search results in Unity dash home.
Install dconf-editor by clicking on this big button:
Or by running this command in a terminal:
sudo apt-get install dconf-tools
Then navigate to com
→ canonical
→ Unity
→ Dash
and change the setting for home-lens-ordering
to ['files.lens', 'applications.lens', 'music.lens']
.
If you would like to get back to the default setting, you can hit the Set to Default button on the lower right corner.
This is what you get once you adjust the setting as above:
Alternatively, if you don't like to hunt with your mouse, you can run this command in a terminal:
gsettings set com.canonical.Unity.Dash home-lens-ordering "['files.lens', 'applications.lens', 'music.lens']"
It will order the results in the way you prefer.
To reset the setting, you run this command:
gsettings reset com.canonical.Unity.Dash home-lens-ordering
Ubuntu 17.10 (and then 18.04) has brought a few changes (for prior versions, see one of the other answers). There are no longer any Amazon/web search results when you search in the Dash, but the Amazon icon remains in the launcher by default. It is part of the ubuntu-web-launchers package, which can be removed with:
sudo apt-get remove ubuntu-web-launchers
At the time of this writing, Amazon appears to be the only thing in the package, so it should be fine to remove. Keep in mind that this might not be the case in the future, so it might be safer to just remove Amazon if you might want to keep other web launchers. Take a look at the list of files in the package and get rid of the Amazon ones:
sudo rm /usr/share/applications/com.canonical.launcher.amazon.desktop
sudo rm /usr/share/applications/ubuntu-amazon-default.desktop
Best Answer
Mark Tully has created a shopping lens independent of Canonical's unity-lens-shopping.
Search results in the independent lens are still Canonical/Amazon affiliated links and purchases made will help fund Ubuntu. To install the independent shopping lens simply run the following two commands in the terminal (Ctrl+Alt+T).
Remove shopping results from the home lens with the terminal command below. This will uninstall Canonical's default shopping lens.
Found on omgubuntu