These instructions are for Ubuntu 12.04 running the Unity desktop on which gnome-session-fallback was installed using either the Ubuntu Software Center or sudo apt-get on the command line.

The instructions may be the same for other versions of Ubuntu, but no guarantee is made.

When gnome-session-fallback is installed in Ubuntu 12.04, it installs several packages and libraries it requires as well as some optional packages. Not all these packages and libraries are uninstalled when you uninstall gnome-session-fallback.

Quick Uninstall

This is not recommended because it will remove all packages normally installed with gnome-session-fallback. This may include packages you previously installed or were installed by other applications.

Note: this uninstall command assumes gnome-session-fallback was installed on a fresh Ubuntu 12.04.

1) Open a terminal (instructions can be found here).

2) Enter the following command (it is very long and a single line):

sudo apt-get purge --auto-remove alacarte gir1.2-panelapplet-4.0 gnome-applets gnome-applets-data gnome-panel  gnome-panel-data gnome-session-fallback indicator-applet-complete  libpanel-applet-4-0 python-gmenu

It is easiest to copy the line and paste it into the terminal (right-click on the terminal and select Paste from the popup menu).

Preferred Uninstall

The better way to uninstall it is to follow the directions on this page.

This will show you on how to uninstall only the packages that were installed when gnome-session-fallback was installed. The instructions are generic and work for any installed package.

It involves:

identifying which packages were installed and
creating a command to uninstall only those packages

It leaves intact any packages you may have installed or were installed by other applications instead of blindly assuming that they were installed along with gnome-session-fallback.