How to disable the beep sound system-wide

Solution for GNOME 2 (Debian 6):

I tried one more thing... System -> Preferences -> Sound. This brings up the Volume Control application:

From there I click on Preferences which brings up another window. I then click on Beep, and that mutes window thus:

I then proceed to clicking on the speaker icon on PCM column, after which I become happy.

Solution for GNOME 3 (Debian 7):

Edit /etc/gdm3/greeter.gsettings such that you have this entry:

# Disabling sound in the greeter
[org.gnome.desktop.sound]
event-sounds=false

You'll probably just have to uncomment the 2 lines. Note that I can't find a way to do something like this as normal user. I guess GNOME 3 killed some configurability.

Gnome Shell (3.22) and Debian 9 (stretch)

Just go to Sound → Sound Effects and turn off the Alert volume like shown below: