Disable Volume Change Feedback
You can turn this sound off from the Sound section of System Preferences, but this is a bit time consuming to do every time you want to quietly change the volume.
Luckily there is a keyboard shortcut to silence the volume changing beep on a case by case basis. If you hold the Shift key while changing the volume, you will get no audio feedback, meaning you won't bother anyone with the clicking sound.
You can also get this to work the other way round. If you turn off the feedback in the Sound section of System Preferences, the clicking sound will only play if you hold down shift before changing the volume.
(This is vaguely related to a previous tip - holding option before pressing the volume change keys will open up the Sound System Preferences.)