How to remove the Unity Amazon package in 16.04?

Removing the unity-webapps-common package removes Amazon from the dash. Since the Amazon webapp is part of that package, you can't just remove the Amazon portion (well, short of editing the source code). This is a problem when other programs (like Unity Tweak Tool) depend on that package.

As noted by fitojb in this answer to another question, however, this command will prevent the Amazon icon from showing up in the dash:

sudo rm -rf /usr/share/applications/ubuntu-amazon-default.desktop

However, as dobey pointed out in a comment below, when the unity-webapps-common package updates the file will be replaced and the command will have to be run again. A more permanent method is to copy the .desktop file to your local applications directory and then add a line to the file to prevent it from showing up in the dash:

echo 'Hidden=true' | cat /usr/share/applications/ubuntu-amazon-default.desktop - > ~/.local/share/applications/ubuntu-amazon-default.desktop

As Aibara Iduas suggests, removing /usr/share/applications/ubuntu-amazon-default.desktop is the solution. But it will come back with the next upgrade. The solution to copy the file to ~/.local/share/applications/ubuntu-amazon-default.desktop works only for the current user. To disable this .desktop file for all users on the machine, and to prevent upgrades from putting it back, the solution is to divert the file with dpkg-divert.

sudo dpkg-divert \
  --divert /usr/share/applications/ubuntu-amazon-default.desktop.diverted \
  --local \
  --rename \
  /usr/share/applications/ubuntu-amazon-default.desktop

In Ubuntu 18.04, just deinstall the ubuntu-web-launchers package:

sudo apt remove ubuntu-web-launchers

It only contains the Amazon launcher, as you can see by doing

dpkg -L ubuntu-web-launchers

first.