For most devices, there is a somewhat secret option in Say Cheese for turning the shutter sound on and off. From the table of contents click the Timer button, and then below the Shutter Delay options there is a Shutter Sound section. Just scroll down and from there you can turn the shutter sound on and off.
If the Say Cheese silent feature does not work on your phone and you are determined to have a silent shutter, you can simply delete the shutter sound file: system/media/audio/ui/camera_click.ogg
You can do this with one of the file managers. But you will need root access to your phone, Also in some countries, like Japan, a silent camera is illegal. Go figure.
Anyway, that's the guaranteed solution. You may want to save a copy of the file in case you want to restore the shutter sound. You can also replace this file with your own shutter sound, which could be interesting.
* On some devices, setting the shutter sound off option will disable the voice response.